Solution 1 to problem l12o35
Expressions |
Parameters |
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Back to problem l12o35
Expressions
The solution is given through the following expressions:
b164=0
1 4 1 4
- -----*a21*a25 *b1 + -----*a21*a25 *b69
243 243
b163=-------------------------------------------
5
a17
b162=0
5 4
----*a25 *b69
81
b161=---------------
4
a17
4 2 3 4 2 3
- -----*a21 *a25 *b1 + -----*a21 *a25 *b69
243 243
b160=---------------------------------------------
5
a17
16 3 16 3
- ----*a21*a25 *b1 + ----*a21*a25 *b69
81 81
b159=-----------------------------------------
4
a17
20 3
----*a21*a25 *b69
81
b158=-------------------
4
a17
4 3 4 3
- ----*a21*a25 *b1 + ----*a21*a25 *b69
81 81
b157=-----------------------------------------
4
a17
b156=0
b155=0
10 3
----*a25 *b69
27
b154=---------------
3
a17
20 3
----*a25 *b69
9
b153=---------------
3
a17
10 3
----*a25 *b69
27
b152=---------------
3
a17
2 3 2 2 3 2
- ----*a21 *a25 *b1 + ----*a21 *a25 *b69
81 81
b151=-------------------------------------------
5
a17
32 2 2 32 2 2
- ----*a21 *a25 *b1 + ----*a21 *a25 *b69
81 81
b150=-------------------------------------------
4
a17
10 2 2
----*a21 *a25 *b69
27
b149=--------------------
4
a17
28 2 2 28 2 2
- ----*a21 *a25 *b1 + ----*a21 *a25 *b69
81 81
b148=-------------------------------------------
4
a17
28 2 28 2
- ----*a21*a25 *b1 + ----*a21*a25 *b69
27 27
b147=-----------------------------------------
3
a17
4 2 4 2
- ---*a21*a25 *b1 + ---*a21*a25 *b69
9 9
b146=---------------------------------------
3
a17
4 2 32 2
- ---*a21*a25 *b1 + ----*a21*a25 *b69
9 27
b145=----------------------------------------
3
a17
40 2
----*a21*a25 *b69
9
b144=-------------------
3
a17
10 2
----*a21*a25 *b69
9
b143=-------------------
3
a17
32 2 32 2
- ----*a21*a25 *b1 + ----*a21*a25 *b69
27 27
b142=-----------------------------------------
3
a17
20 2
----*a21*a25 *b69
9
b141=-------------------
3
a17
2 2 8 2
----*a21*a25 *b1 + ----*a21*a25 *b69
27 27
b140=--------------------------------------
3
a17
8 2 8 2
- ----*a21*a25 *b1 + ----*a21*a25 *b69
27 27
b139=-----------------------------------------
3
a17
b138=0
b137=0
40 2
----*a25 *b69
9
b136=---------------
2
a17
20 2
----*a25 *b69
9
b135=---------------
2
a17
20 2
----*a25 *b69
3
b134=---------------
2
a17
40 2
----*a25 *b69
9
b133=---------------
2
a17
40 2
----*a25 *b69
9
b132=---------------
2
a17
20 2
----*a25 *b69
3
b131=---------------
2
a17
10 2
----*a25 *b69
9
b130=---------------
2
a17
4 4 4 4
- -----*a21 *a25*b1 + -----*a21 *a25*b69
243 243
b129=-------------------------------------------
5
a17
16 3 16 3
- ----*a21 *a25*b1 + ----*a21 *a25*b69
81 81
b128=-----------------------------------------
4
a17
20 3
----*a21 *a25*b69
81
b127=-------------------
4
a17
44 3 44 3
- ----*a21 *a25*b1 + ----*a21 *a25*b69
81 81
b126=-----------------------------------------
4
a17
4 2 4 2
- ---*a21 *a25*b1 + ---*a21 *a25*b69
9 9
b125=---------------------------------------
3
a17
4 2 22 2
- ---*a21 *a25*b1 + ----*a21 *a25*b69
9 27
b124=----------------------------------------
3
a17
20 2
----*a21 *a25*b69
9
b123=-------------------
3
a17
10 2
----*a21 *a25*b69
9
b122=-------------------
3
a17
88 2 88 2
- ----*a21 *a25*b1 + ----*a21 *a25*b69
27 27
b121=-----------------------------------------
3
a17
40 2
----*a21 *a25*b69
9
b120=-------------------
3
a17
40 2 20 2
- ----*a21 *a25*b1 + ----*a21 *a25*b69
27 9
b119=-----------------------------------------
3
a17
28 2 28 2
- ----*a21 *a25*b1 + ----*a21 *a25*b69
27 27
b118=-----------------------------------------
3
a17
4 4
- ---*a21*a25*b1 + ---*a21*a25*b69
9 9
b117=-------------------------------------
2
a17
4 32
- ---*a21*a25*b1 + ----*a21*a25*b69
3 9
b116=--------------------------------------
2
a17
40
----*a21*a25*b69
9
b115=------------------
2
a17
40
----*a21*a25*b69
9
b114=------------------
2
a17
20
----*a21*a25*b69
3
b113=------------------
2
a17
20
----*a21*a25*b69
9
b112=------------------
2
a17
4 4
- ---*a21*a25*b1 + ---*a21*a25*b69
3 3
b111=-------------------------------------
2
a17
4 52
- ---*a21*a25*b1 + ----*a21*a25*b69
3 9
b110=--------------------------------------
2
a17
40
----*a21*a25*b69
3
b109=------------------
2
a17
20
----*a21*a25*b69
3
b108=------------------
2
a17
4 28
---*a21*a25*b1 + ----*a21*a25*b69
3 9
b107=-----------------------------------
2
a17
40
----*a21*a25*b69
9
b106=------------------
2
a17
28 28
- ----*a21*a25*b1 + ----*a21*a25*b69
9 9
b105=---------------------------------------
2
a17
40
----*a21*a25*b69
9
b104=------------------
2
a17
2
---*a21*a25*b1 + 2*a21*a25*b69
9
b103=--------------------------------
2
a17
2 2
- ---*a21*a25*b1 + ---*a21*a25*b69
3 3
b102=-------------------------------------
2
a17
b101=0
10
----*a25*b69
3
b100=--------------
a17
5
---*a25*b69
3
b99=-------------
a17
10
----*a25*b69
3
b98=--------------
a17
10*a25*b69
b97=------------
a17
20
----*a25*b69
3
b96=--------------
a17
20
----*a25*b69
3
b95=--------------
a17
20
----*a25*b69
3
b94=--------------
a17
5
---*a25*b69
3
b93=-------------
a17
1 5 1 5
- -----*a21 *b1 + -----*a21 *b69
243 243
b92=-----------------------------------
5
a17
5 4
----*a21 *b69
81
b91=---------------
4
a17
20 4 20 4
- ----*a21 *b1 + ----*a21 *b69
81 81
b90=---------------------------------
4
a17
10 3
----*a21 *b69
27
b89=---------------
3
a17
20 3
----*a21 *b69
9
b88=---------------
3
a17
70 3 80 3
- ----*a21 *b1 + ----*a21 *b69
27 27
b87=---------------------------------
3
a17
20 3 20 3
- ----*a21 *b1 + ----*a21 *b69
27 27
b86=---------------------------------
3
a17
10 2
----*a21 *b69
9
b85=---------------
2
a17
20 2
----*a21 *b69
3
b84=---------------
2
a17
100 2
-----*a21 *b69
9
b83=----------------
2
a17
40 2
----*a21 *b69
9
b82=---------------
2
a17
40 2
----*a21 *b69
9
b81=---------------
2
a17
50 2 70 2
- ----*a21 *b1 + ----*a21 *b69
9 9
b80=---------------------------------
2
a17
10 2 10 2
- ----*a21 *b1 + ----*a21 *b69
9 9
b79=---------------------------------
2
a17
5
---*a21*b69
3
b78=-------------
a17
20
----*a21*b69
3
b77=--------------
a17
20
----*a21*b69
3
b76=--------------
a17
20
----*a21*b69
3
b75=--------------
a17
10*a21*b69
b74=------------
a17
1
- ---*a21*b1 + 2*a21*b69
3
b73=---------------------------
a17
10
----*a21*b69
3
b72=--------------
a17
2 8
---*a21*b1 + ---*a21*b69
3 3
b71=--------------------------
a17
2 2
- ---*a21*b1 + ---*a21*b69
3 3
b70=-----------------------------
a17
1 5 1 5
-----*a25 *b1 - -----*a25 *b69
243 243
b68=--------------------------------
5
a17
4 4 4 4
-----*a21*a25 *b1 - -----*a21*a25 *b69
243 243
b67=----------------------------------------
5
a17
20 4 20 4
----*a25 *b1 - ----*a25 *b69
81 81
b66=------------------------------
4
a17
5 4
----*a25 *b1
81
b65=--------------
4
a17
2 2 3 2 2 3
----*a21 *a25 *b1 - ----*a21 *a25 *b69
81 81
b64=----------------------------------------
5
a17
44 3 44 3
----*a21*a25 *b1 - ----*a21*a25 *b69
81 81
b63=--------------------------------------
4
a17
4 3 16 3
---*a21*a25 *b1 - ----*a21*a25 *b69
9 81
b62=-------------------------------------
4
a17
20 3 20 3
----*a25 *b1 - ----*a25 *b69
9 9
b61=------------------------------
3
a17
20 3 20 3
----*a25 *b1 - ----*a25 *b69
27 27
b60=------------------------------
3
a17
20 3 10 3
----*a25 *b1 - ----*a25 *b69
27 27
b59=------------------------------
3
a17
20 3
----*a25 *b1
9
b58=--------------
3
a17
10 3
----*a25 *b1
27
b57=--------------
3
a17
4 3 2 4 3 2
-----*a21 *a25 *b1 - -----*a21 *a25 *b69
243 243
b56=------------------------------------------
5
a17
28 2 2 28 2 2
----*a21 *a25 *b1 - ----*a21 *a25 *b69
81 81
b55=----------------------------------------
4
a17
62 2 2 32 2 2
----*a21 *a25 *b1 - ----*a21 *a25 *b69
81 81
b54=----------------------------------------
4
a17
32 2 32 2
----*a21*a25 *b1 - ----*a21*a25 *b69
27 27
b53=--------------------------------------
3
a17
28 2 28 2
----*a21*a25 *b1 - ----*a21*a25 *b69
27 27
b52=--------------------------------------
3
a17
28 2 8 2
----*a21*a25 *b1 - ----*a21*a25 *b69
27 27
b51=--------------------------------------
3
a17
208 2 88 2
-----*a21*a25 *b1 - ----*a21*a25 *b69
27 27
b50=---------------------------------------
3
a17
82 2 4 2
----*a21*a25 *b1 - ---*a21*a25 *b69
27 9
b49=-------------------------------------
3
a17
14 2 4 2
----*a21*a25 *b1 - ---*a21*a25 *b69
9 9
b48=-------------------------------------
3
a17
40 2 40 2
----*a25 *b1 - ----*a25 *b69
9 9
b47=------------------------------
2
a17
10 2 10 2
----*a25 *b1 - ----*a25 *b69
9 9
b46=------------------------------
2
a17
40 2
----*a25 *b1
9
b45=--------------
2
a17
10 2 10 2
----*a25 *b1 - ----*a25 *b69
3 9
b44=------------------------------
2
a17
20 2
----*a25 *b1
3
b43=--------------
2
a17
40 2
----*a25 *b1
9
b42=--------------
2
a17
40 2
----*a25 *b1
9
b41=--------------
2
a17
20 2
----*a25 *b1
3
b40=--------------
2
a17
10 2
----*a25 *b1
9
b39=--------------
2
a17
1 4 1 4
-----*a21 *a25*b1 - -----*a21 *a25*b69
243 243
b38=----------------------------------------
5
a17
4 3 4 3
----*a21 *a25*b1 - ----*a21 *a25*b69
81 81
b37=--------------------------------------
4
a17
4 3 16 3
---*a21 *a25*b1 - ----*a21 *a25*b69
9 81
b36=-------------------------------------
4
a17
8 2 8 2
----*a21 *a25*b1 - ----*a21 *a25*b69
27 27
b35=--------------------------------------
3
a17
8 2 2 2
----*a21 *a25*b1 + ----*a21 *a25*b69
27 27
b34=--------------------------------------
3
a17
92 2 32 2
----*a21 *a25*b1 - ----*a21 *a25*b69
27 27
b33=--------------------------------------
3
a17
20 2 40 2
----*a21 *a25*b1 - ----*a21 *a25*b69
3 27
b32=--------------------------------------
3
a17
14 2 4 2
----*a21 *a25*b1 - ---*a21 *a25*b69
9 9
b31=-------------------------------------
3
a17
2 2
---*a21*a25*b1 - ---*a21*a25*b69
3 3
b30=----------------------------------
2
a17
2
2*a21*a25*b1 + ---*a21*a25*b69
9
b29=--------------------------------
2
a17
68 28
----*a21*a25*b1 - ----*a21*a25*b69
9 9
b28=------------------------------------
2
a17
68 4
----*a21*a25*b1 + ---*a21*a25*b69
9 3
b27=-----------------------------------
2
a17
172 4
-----*a21*a25*b1 - ---*a21*a25*b69
9 3
b26=------------------------------------
2
a17
40
----*a21*a25*b1
9
b25=-----------------
2
a17
4
8*a21*a25*b1 - ---*a21*a25*b69
3
b24=--------------------------------
2
a17
44 4
----*a21*a25*b1 - ---*a21*a25*b69
3 3
b23=-----------------------------------
2
a17
8 4
---*a21*a25*b1 - ---*a21*a25*b69
3 9
b22=----------------------------------
2
a17
2 2
---*a25*b1 - ---*a25*b69
3 3
b21=--------------------------
a17
8 2
---*a25*b1 + ---*a25*b69
3 3
b20=--------------------------
a17
1
2*a25*b1 - ---*a25*b69
3
b19=------------------------
a17
10
----*a25*b1
3
b18=-------------
a17
10*a25*b1
b17=-----------
a17
20
----*a25*b1
3
b16=-------------
a17
20
----*a25*b1
3
b15=-------------
a17
20
----*a25*b1
3
b14=-------------
a17
5
---*a25*b1
3
b13=------------
a17
b12=0
5 4
----*a21 *b1
81
b11=--------------
4
a17
70 3
----*a21 *b1
27
b10=--------------
3
a17
10 3
----*a21 *b1
27
b9=--------------
3
a17
140 2
-----*a21 *b1
9
b8=---------------
2
a17
40 2
----*a21 *b1
3
b7=--------------
2
a17
10 2
----*a21 *b1
9
b6=--------------
2
a17
50
----*a21*b1
3
b5=-------------
a17
25
----*a21*b1
3
b4=-------------
a17
40
----*a21*b1
3
b3=-------------
a17
5
---*a21*b1
3
b2=------------
a17
a36=0
- a16*a21
a35=------------
a25
a34=0
1 2
---*a25
3
a33=----------
a17
2
- 2*a16*a21
a32=---------------
2
a25
- 12*a16*a17*a21
a31=-------------------
2
a25
2
---*a21*a25
3
a30=-------------
a17
- 6*a16*a17*a21
a29=------------------
2
a25
a28=0
a27=a25
a26=2*a25
3
- a16*a21
a24=-------------
3
a25
1 2
---*a21
3
a23=----------
a17
2
- 18*a16*a17*a21
a22=--------------------
3
a25
a20=2*a21
2 3
9*a16*a17 *a21 + a21*a25
a19=---------------------------
3
a25
2
- 18*a16*a17 *a21
a18=--------------------
3
a25
2*a16*a21
a15=-----------
a25
18*a16*a17
a14=------------
a25
2 1 3
9*a16*a17 + ---*a25
3
a13=-----------------------
a17*a25
2
a16*a21
a12=----------
2
a25
6*a16*a17*a21
a11=---------------
2
a25
2 2 3
30*a16*a17 *a21 + ---*a21*a25
3
a10=--------------------------------
2
a17*a25
2
18*a16*a17
a9=-------------
2
a25
2 3
18*a16*a17 + a25
a8=--------------------
2
a25
2 3
54*a16*a17 + 2*a25
a7=----------------------
2
a25
2 3
27*a16*a17 + a25
a6=--------------------
2
a25
a5=0
2 2 1 2 3
9*a16*a17 *a21 + ---*a21 *a25
3
a4=---------------------------------
3
a17*a25
2 3
81*a16*a17 *a21 + 3*a21*a25
a3=------------------------------
3
a25
2 3
27*a16*a17 *a21 + a21*a25
a2=----------------------------
3
a25
3 3
27*a16*a17 + a17*a25
a1=------------------------
3
a25
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
b69,b1,a16,a21,a25,a17
Relevance for the application:
The solution given above tells us that the system {u_s, v_s}
is a higher order symmetry for the lower order system {u_t,v_t}
where u=u(t,x) is a scalar function, v=v(t,x) is a vector
function of arbitrary dimension and f(..,..) is the scalar
product between two such vectors:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
4 2 3 3
df(u,t)=(27*u *a16*a17 + u *a17 *a25 + 27*u *f(v,v)*a16*a17 *a25
3x 3x 2x
4 3 2 3 2
+ u *f(v,v)*a17*a25 + 27*u *a16*a17 *a21*u + u *a17*a21*a25 *u
2x 2x 2x
2 3 2 3
+ 81*u *a16*a17 *a21*u + 3*u *a17*a21*a25 *u
x x
3 4
+ 54*u *f(v,v )*a16*a17 *a25 + 2*u *f(v,v )*a17*a25
x x x x
2 2 2 1 2 5
+ 9*u *f(v,v) *a16*a17 *a25 + ---*u *f(v,v) *a25
x 3 x
2 2 2 4 2
+ 30*u *f(v,v)*a16*a17 *a21*a25*u + ---*u *f(v,v)*a21*a25 *u
x 3 x
2 2 4 1 2 3 4
+ 9*u *a16*a17 *a21 *u + ---*u *a21 *a25 *u
x 3 x
3 4
+ 18*f(v ,v )*a16*a17 *a25*u + f(v ,v )*a17*a25 *u
x x x x
3 2 2
+ 18*f(v,v )*a16*a17 *a25*u + 18*f(v,v )*f(v,v)*a16*a17 *a25 *u
2x x
2 3 3 3
+ 6*f(v,v )*a16*a17 *a21*a25*u + f(v,v) *a16*a17*a25 *u
x
2 2 3 2 5
+ 2*f(v,v) *a16*a17*a21*a25 *u + f(v,v)*a16*a17*a21 *a25*u )/(a17
3
*a25 )
5 5 4 5 4 2
df(u,s)=(u *a17 *b1 + ---*u *f(v,v)*a17 *a25*b1 + ---*u *a17 *a21*b1*u
5x 3 4x 3 4x
40 4 20 4
+ ----*u *u *a17 *a21*b1*u + ----*u *f(v,v )*a17 *a25*b1
3 3x x 3 3x x
10 2 3 2 8 3 2
+ ----*u *f(v,v) *a17 *a25 *b1 + ---*u *f(v,v)*a17 *a21*a25*b1*u
9 3x 3 3x
4 3 2 10 3 2 4
- ---*u *f(v,v)*a17 *a21*a25*b69*u + ----*u *a17 *a21 *b1*u
9 3x 9 3x
25 2 4 50 2 4
+ ----*u *a17 *a21*b1*u + ----*u *u *a17 *a21*b1
3 2x 3 2x x
44 3
+ ----*u *u *f(v,v)*a17 *a21*a25*b1*u
3 2x x
4 3 40 3 2 3
- ---*u *u *f(v,v)*a17 *a21*a25*b69*u + ----*u *u *a17 *a21 *b1*u
3 2x x 3 2x x
20 4 20 4
+ ----*u *f(v ,v )*a17 *a25*b1 + ----*u *f(v,v )*a17 *a25*b1
3 2x x x 3 2x 2x
20 3 2
+ ----*u *f(v,v )*f(v,v)*a17 *a25 *b1
3 2x x
3 2
+ 8*u *f(v,v )*a17 *a21*a25*b1*u
2x x
4 3 2 10 3 2 3
- ---*u *f(v,v )*a17 *a21*a25*b69*u + ----*u *f(v,v) *a17 *a25 *b1
3 2x x 27 2x
14 2 2 2 2
+ ----*u *f(v,v) *a17 *a21*a25 *b1*u
9 2x
4 2 2 2 2
- ---*u *f(v,v) *a17 *a21*a25 *b69*u
9 2x
14 2 2 4
+ ----*u *f(v,v)*a17 *a21 *a25*b1*u
9 2x
4 2 2 4 10 2 3 6
- ---*u *f(v,v)*a17 *a21 *a25*b69*u + ----*u *a17 *a21 *b1*u
9 2x 27 2x
40 3 3 140 3 3 2 2
+ ----*u *f(v,v)*a17 *a21*a25*b1 + -----*u *a17 *a21 *b1*u
9 x 9 x
172 2 3
+ -----*u *f(v,v )*a17 *a21*a25*b1*u
9 x x
4 2 3
- ---*u *f(v,v )*a17 *a21*a25*b69*u
3 x x
82 2 2 2 2
+ ----*u *f(v,v) *a17 *a21*a25 *b1*u
27 x
4 2 2 2 2
- ---*u *f(v,v) *a17 *a21*a25 *b69*u
9 x
20 2 2 2 3
+ ----*u *f(v,v)*a17 *a21 *a25*b1*u
3 x
40 2 2 2 3 70 2 2 3 5
- ----*u *f(v,v)*a17 *a21 *a25*b69*u + ----*u *a17 *a21 *b1*u
27 x 27 x
4 40 3 2
+ 10*u *f(v ,v )*a17 *a25*b1 + ----*u *f(v ,v )*f(v,v)*a17 *a25 *b1
x x 2x 9 x x x
68 3 2
+ ----*u *f(v ,v )*a17 *a21*a25*b1*u
9 x x x
4 3 2 10 4
+ ---*u *f(v ,v )*a17 *a21*a25*b69*u + ----*u *f(v,v )*a17 *a25*b1
3 x x x 3 x 3x
40 3 2
+ ----*u *f(v,v )*f(v,v)*a17 *a25 *b1
9 x 2x
68 3 2
+ ----*u *f(v,v )*a17 *a21*a25*b1*u
9 x 2x
28 3 2 20 2 3 2
- ----*u *f(v,v )*a17 *a21*a25*b69*u + ----*u *f(v,v ) *a17 *a25 *b1
9 x 2x 3 x x
20 2 2 3
+ ----*u *f(v,v )*f(v,v) *a17 *a25 *b1
9 x x
208 2 2 2
+ -----*u *f(v,v )*f(v,v)*a17 *a21*a25 *b1*u
27 x x
88 2 2 2
- ----*u *f(v,v )*f(v,v)*a17 *a21*a25 *b69*u
27 x x
92 2 2 4
+ ----*u *f(v,v )*a17 *a21 *a25*b1*u
27 x x
32 2 2 4 5 4 4
- ----*u *f(v,v )*a17 *a21 *a25*b69*u + ----*u *f(v,v) *a17*a25 *b1
27 x x 81 x
4 3 3 2
+ ---*u *f(v,v) *a17*a21*a25 *b1*u
9 x
16 3 3 2
- ----*u *f(v,v) *a17*a21*a25 *b69*u
81 x
62 2 2 2 4
+ ----*u *f(v,v) *a17*a21 *a25 *b1*u
81 x
32 2 2 2 4
- ----*u *f(v,v) *a17*a21 *a25 *b69*u
81 x
4 3 6
+ ---*u *f(v,v)*a17*a21 *a25*b1*u
9 x
16 3 6 5 4 8
- ----*u *f(v,v)*a17*a21 *a25*b69*u + ----*u *a17*a21 *b1*u
81 x 81 x
4 1 4
+ 2*f(v ,v )*a17 *a25*b1*u - ---*f(v ,v )*a17 *a25*b69*u
2x 2x 3 2x 2x
8 4 2 4
+ ---*f(v ,v )*a17 *a25*b1*u + ---*f(v ,v )*a17 *a25*b69*u
3 x 3x 3 x 3x
10 3 2
+ ----*f(v ,v )*f(v,v)*a17 *a25 *b1*u
3 x 2x
10 3 2
- ----*f(v ,v )*f(v,v)*a17 *a25 *b69*u
9 x 2x
3 3 2 3 3
+ 2*f(v ,v )*a17 *a21*a25*b1*u + ---*f(v ,v )*a17 *a21*a25*b69*u
x 2x 9 x 2x
40 3 2
+ ----*f(v ,v )*f(v,v )*a17 *a25 *b1*u
9 x x x
20 2 2 3
+ ----*f(v ,v )*f(v,v) *a17 *a25 *b1*u
27 x x
10 2 2 3
- ----*f(v ,v )*f(v,v) *a17 *a25 *b69*u
27 x x
28 2 2 3
+ ----*f(v ,v )*f(v,v)*a17 *a21*a25 *b1*u
27 x x
8 2 2 3
- ----*f(v ,v )*f(v,v)*a17 *a21*a25 *b69*u
27 x x
8 2 2 5
+ ----*f(v ,v )*a17 *a21 *a25*b1*u
27 x x
2 2 2 5 2 4
+ ----*f(v ,v )*a17 *a21 *a25*b69*u + ---*f(v,v )*a17 *a25*b1*u
27 x x 3 4x
2 4 10 3 2
- ---*f(v,v )*a17 *a25*b69*u + ----*f(v,v )*f(v,v)*a17 *a25 *b1*u
3 4x 9 3x
10 3 2
- ----*f(v,v )*f(v,v)*a17 *a25 *b69*u
9 3x
2 3 3 2 3 3
+ ---*f(v,v )*a17 *a21*a25*b1*u - ---*f(v,v )*a17 *a21*a25*b69*u
3 3x 3 3x
40 3 2
+ ----*f(v,v )*f(v,v )*a17 *a25 *b1*u
9 2x x
40 3 2
- ----*f(v,v )*f(v,v )*a17 *a25 *b69*u
9 2x x
20 2 2 3
+ ----*f(v,v )*f(v,v) *a17 *a25 *b1*u
27 2x
20 2 2 3
- ----*f(v,v )*f(v,v) *a17 *a25 *b69*u
27 2x
28 2 2 3
+ ----*f(v,v )*f(v,v)*a17 *a21*a25 *b1*u
27 2x
28 2 2 3
- ----*f(v,v )*f(v,v)*a17 *a21*a25 *b69*u
27 2x
8 2 2 5
+ ----*f(v,v )*a17 *a21 *a25*b1*u
27 2x
8 2 2 5
- ----*f(v,v )*a17 *a21 *a25*b69*u
27 2x
20 2 2 3
+ ----*f(v,v ) *f(v,v)*a17 *a25 *b1*u
9 x
20 2 2 3
- ----*f(v,v ) *f(v,v)*a17 *a25 *b69*u
9 x
32 2 2 2 3
+ ----*f(v,v ) *a17 *a21*a25 *b1*u
27 x
32 2 2 2 3
- ----*f(v,v ) *a17 *a21*a25 *b69*u
27 x
20 3 4
+ ----*f(v,v )*f(v,v) *a17*a25 *b1*u
81 x
20 3 4
- ----*f(v,v )*f(v,v) *a17*a25 *b69*u
81 x
44 2 3 3
+ ----*f(v,v )*f(v,v) *a17*a21*a25 *b1*u
81 x
44 2 3 3
- ----*f(v,v )*f(v,v) *a17*a21*a25 *b69*u
81 x
28 2 2 5
+ ----*f(v,v )*f(v,v)*a17*a21 *a25 *b1*u
81 x
28 2 2 5
- ----*f(v,v )*f(v,v)*a17*a21 *a25 *b69*u
81 x
4 3 7 4 3 7
+ ----*f(v,v )*a17*a21 *a25*b1*u - ----*f(v,v )*a17*a21 *a25*b69*u
81 x 81 x
1 5 5 1 5 5
+ -----*f(v,v) *a25 *b1*u - -----*f(v,v) *a25 *b69*u
243 243
4 4 4 3 4 4 4 3
+ -----*f(v,v) *a21*a25 *b1*u - -----*f(v,v) *a21*a25 *b69*u
243 243
2 3 2 3 5 2 3 2 3 5
+ ----*f(v,v) *a21 *a25 *b1*u - ----*f(v,v) *a21 *a25 *b69*u
81 81
4 2 3 2 7 4 2 3 2 7
+ -----*f(v,v) *a21 *a25 *b1*u - -----*f(v,v) *a21 *a25 *b69*u
243 243
1 4 9 1 4 9 5
+ -----*f(v,v)*a21 *a25*b1*u - -----*f(v,v)*a21 *a25*b69*u )/a17
243 243
3 2 3 2 3
df(v,t)=( - 18*u *a16*a17 *a21*u*v + 9*u *a16*a17 *a21*v + u *a17*a21*a25 *v
2x x x
3 2
+ 2*u *v *a17*a21*a25 *u - 6*u *f(v,v)*a16*a17 *a21*a25*u*v
x x x
2 2 3 2 3 4
- 18*u *a16*a17 *a21 *u *v + v *a17 *a25 + v *f(v,v)*a17*a25
x 3x 2x
3 2 4 1 2 5
+ v *a17*a21*a25 *u + 2*v *f(v,v )*a17*a25 + ---*v *f(v,v) *a25
2x x x 3 x
2 4 2 1 2 3 4
+ ---*v *f(v,v)*a21*a25 *u + ---*v *a21 *a25 *u
3 x 3 x
4 2 2
+ f(v ,v )*a17*a25 *v - 12*f(v,v )*a16*a17 *a21*a25*u *v
x x x
2 2 2 2 4
- f(v,v) *a16*a17*a21*a25 *u *v - 2*f(v,v)*a16*a17*a21 *a25*u *v
3 6 3
- a16*a17*a21 *u *v)/(a17*a25 )
2 4 2 4
df(v,s)=( - ---*u *a17 *a21*b1*u*v + ---*u *a17 *a21*b69*u*v
3 4x 3 4x
2 4 8 4
+ ---*u *u *a17 *a21*b1*v + ---*u *u *a17 *a21*b69*v
3 3x x 3 3x x
10 4 2 3
+ ----*u *v *a17 *a21*b69*u - ---*u *f(v,v)*a17 *a21*a25*b1*u*v
3 3x x 3 3x
2 3 10 3 2 3
+ ---*u *f(v,v)*a17 *a21*a25*b69*u*v - ----*u *a17 *a21 *b1*u *v
3 3x 9 3x
10 3 2 3 1 2 4
+ ----*u *a17 *a21 *b69*u *v - ---*u *a17 *a21*b1*v
9 3x 3 2x
2 4 4
+ 2*u *a17 *a21*b69*v + 10*u *u *v *a17 *a21*b69
2x 2x x x
2 3
+ ---*u *u *f(v,v)*a17 *a21*a25*b1*v
9 2x x
3 50 3 2 2
+ 2*u *u *f(v,v)*a17 *a21*a25*b69*v - ----*u *u *a17 *a21 *b1*u *v
2x x 9 2x x
70 3 2 2 20 4
+ ----*u *u *a17 *a21 *b69*u *v + ----*u *v *a17 *a21*b69*u
9 2x x 3 2x 2x
40 3 40 3 2 3
+ ----*u *v *f(v,v)*a17 *a21*a25*b69*u + ----*u *v *a17 *a21 *b69*u
9 2x x 9 2x x
28 3
- ----*u *f(v,v )*a17 *a21*a25*b1*u*v
9 2x x
28 3
+ ----*u *f(v,v )*a17 *a21*a25*b69*u*v
9 2x x
8 2 2 2
- ----*u *f(v,v) *a17 *a21*a25 *b1*u*v
27 2x
8 2 2 2
+ ----*u *f(v,v) *a17 *a21*a25 *b69*u*v
27 2x
28 2 2 3
- ----*u *f(v,v)*a17 *a21 *a25*b1*u *v
27 2x
28 2 2 3 20 2 3 5
+ ----*u *f(v,v)*a17 *a21 *a25*b69*u *v - ----*u *a17 *a21 *b1*u *v
27 2x 27 2x
20 2 3 5 40 3 3 2
+ ----*u *a17 *a21 *b69*u *v + ----*u *a17 *a21 *b69*u*v
27 2x 9 x
20 2 4 40 2 3
+ ----*u *v *a17 *a21*b69 + ----*u *v *f(v,v)*a17 *a21*a25*b69
3 x 2x 9 x x
100 2 3 2 2 4 2 3
+ -----*u *v *a17 *a21 *b69*u + ---*u *f(v,v )*a17 *a21*a25*b1*v
9 x x 3 x x
28 2 3
+ ----*u *f(v,v )*a17 *a21*a25*b69*v
9 x x
2 2 2 2 2
+ ----*u *f(v,v) *a17 *a21*a25 *b1*v
27 x
8 2 2 2 2
+ ----*u *f(v,v) *a17 *a21*a25 *b69*v
27 x
40 2 2 2 2
- ----*u *f(v,v)*a17 *a21 *a25*b1*u *v
27 x
20 2 2 2 2 70 2 2 3 4
+ ----*u *f(v,v)*a17 *a21 *a25*b69*u *v - ----*u *a17 *a21 *b1*u *v
9 x 27 x
80 2 2 3 4 20 4
+ ----*u *a17 *a21 *b69*u *v + ----*u *v *a17 *a21*b69*u
27 x 3 x 3x
20 3 20 3 2 3
+ ----*u *v *f(v,v)*a17 *a21*a25*b69*u + ----*u *v *a17 *a21 *b69*u
3 x 2x 3 x 2x
40 3
+ ----*u *v *f(v,v )*a17 *a21*a25*b69*u
3 x x x
20 2 2 2
+ ----*u *v *f(v,v) *a17 *a21*a25 *b69*u
9 x x
40 2 2 3 20 2 3 5
+ ----*u *v *f(v,v)*a17 *a21 *a25*b69*u + ----*u *v *a17 *a21 *b69*u
9 x x 9 x x
4 3
- ---*u *f(v ,v )*a17 *a21*a25*b1*u*v
3 x x x
52 3
+ ----*u *f(v ,v )*a17 *a21*a25*b69*u*v
9 x x x
4 3
- ---*u *f(v,v )*a17 *a21*a25*b1*u*v
3 x 2x
4 3
+ ---*u *f(v,v )*a17 *a21*a25*b69*u*v
3 x 2x
32 2 2
- ----*u *f(v,v )*f(v,v)*a17 *a21*a25 *b1*u*v
27 x x
32 2 2
+ ----*u *f(v,v )*f(v,v)*a17 *a21*a25 *b69*u*v
27 x x
88 2 2 3
- ----*u *f(v,v )*a17 *a21 *a25*b1*u *v
27 x x
88 2 2 3
+ ----*u *f(v,v )*a17 *a21 *a25*b69*u *v
27 x x
4 3 3
- ----*u *f(v,v) *a17*a21*a25 *b1*u*v
81 x
4 3 3
+ ----*u *f(v,v) *a17*a21*a25 *b69*u*v
81 x
28 2 2 2 3
- ----*u *f(v,v) *a17*a21 *a25 *b1*u *v
81 x
28 2 2 2 3
+ ----*u *f(v,v) *a17*a21 *a25 *b69*u *v
81 x
44 3 5
- ----*u *f(v,v)*a17*a21 *a25*b1*u *v
81 x
44 3 5 20 4 7
+ ----*u *f(v,v)*a17*a21 *a25*b69*u *v - ----*u *a17*a21 *b1*u *v
81 x 81 x
20 4 7 5
+ ----*u *a17*a21 *b69*u *v + v *a17 *b69
81 x 5x
5 4 5 4 2
+ ---*v *f(v,v)*a17 *a25*b69 + ---*v *a17 *a21*b69*u
3 4x 3 4x
20 4 10 2 3 2
+ ----*v *f(v,v )*a17 *a25*b69 + ----*v *f(v,v) *a17 *a25 *b69
3 3x x 9 3x
20 3 2 10 3 2 4
+ ----*v *f(v,v)*a17 *a21*a25*b69*u + ----*v *a17 *a21 *b69*u
9 3x 9 3x
20 4 20 4
+ ----*v *f(v ,v )*a17 *a25*b69 + ----*v *f(v,v )*a17 *a25*b69
3 2x x x 3 2x 2x
20 3 2
+ ----*v *f(v,v )*f(v,v)*a17 *a25 *b69
3 2x x
20 3 2
+ ----*v *f(v,v )*a17 *a21*a25*b69*u
3 2x x
10 3 2 3
+ ----*v *f(v,v) *a17 *a25 *b69
27 2x
10 2 2 2 2
+ ----*v *f(v,v) *a17 *a21*a25 *b69*u
9 2x
10 2 2 4 10 2 3 6
+ ----*v *f(v,v)*a17 *a21 *a25*b69*u + ----*v *a17 *a21 *b69*u
9 2x 27 2x
4 40 3 2
+ 10*v *f(v ,v )*a17 *a25*b69 + ----*v *f(v ,v )*f(v,v)*a17 *a25 *b69
x x 2x 9 x x x
40 3 2 10 4
+ ----*v *f(v ,v )*a17 *a21*a25*b69*u + ----*v *f(v,v )*a17 *a25*b69
9 x x x 3 x 3x
40 3 2
+ ----*v *f(v,v )*f(v,v)*a17 *a25 *b69
9 x 2x
40 3 2
+ ----*v *f(v,v )*a17 *a21*a25*b69*u
9 x 2x
20 2 3 2
+ ----*v *f(v,v ) *a17 *a25 *b69
3 x x
20 2 2 3
+ ----*v *f(v,v )*f(v,v) *a17 *a25 *b69
9 x x
40 2 2 2
+ ----*v *f(v,v )*f(v,v)*a17 *a21*a25 *b69*u
9 x x
20 2 2 4 5 4 4
+ ----*v *f(v,v )*a17 *a21 *a25*b69*u + ----*v *f(v,v) *a17*a25 *b69
9 x x 81 x
20 3 3 2
+ ----*v *f(v,v) *a17*a21*a25 *b69*u
81 x
10 2 2 2 4
+ ----*v *f(v,v) *a17*a21 *a25 *b69*u
27 x
20 3 6 5 4 8
+ ----*v *f(v,v)*a17*a21 *a25*b69*u + ----*v *a17*a21 *b69*u
81 x 81 x
5 4 10 4
+ ---*f(v ,v )*a17 *a25*b69*v + ----*f(v ,v )*a17 *a25*b69*v
3 2x 2x 3 x 3x
20 3 2
+ ----*f(v ,v )*f(v,v)*a17 *a25 *b69*v
9 x 2x
4 3 2
- ---*f(v ,v )*a17 *a21*a25*b1*u *v
3 x 2x
32 3 2
+ ----*f(v ,v )*a17 *a21*a25*b69*u *v
9 x 2x
40 3 2
+ ----*f(v ,v )*f(v,v )*a17 *a25 *b69*v
9 x x x
10 2 2 3
+ ----*f(v ,v )*f(v,v) *a17 *a25 *b69*v
27 x x
4 2 2 2
- ---*f(v ,v )*f(v,v)*a17 *a21*a25 *b1*u *v
9 x x
32 2 2 2
+ ----*f(v ,v )*f(v,v)*a17 *a21*a25 *b69*u *v
27 x x
4 2 2 4
- ---*f(v ,v )*a17 *a21 *a25*b1*u *v
9 x x
22 2 2 4
+ ----*f(v ,v )*a17 *a21 *a25*b69*u *v
27 x x
4 3 2
- ---*f(v,v )*a17 *a21*a25*b1*u *v
9 3x
4 3 2
+ ---*f(v,v )*a17 *a21*a25*b69*u *v
9 3x
4 2 2 2
- ---*f(v,v )*f(v,v)*a17 *a21*a25 *b1*u *v
9 2x
4 2 2 2
+ ---*f(v,v )*f(v,v)*a17 *a21*a25 *b69*u *v
9 2x
4 2 2 4
- ---*f(v,v )*a17 *a21 *a25*b1*u *v
9 2x
4 2 2 4
+ ---*f(v,v )*a17 *a21 *a25*b69*u *v
9 2x
28 2 2 2 2
- ----*f(v,v ) *a17 *a21*a25 *b1*u *v
27 x
28 2 2 2 2
+ ----*f(v,v ) *a17 *a21*a25 *b69*u *v
27 x
16 2 3 2
- ----*f(v,v )*f(v,v) *a17*a21*a25 *b1*u *v
81 x
16 2 3 2
+ ----*f(v,v )*f(v,v) *a17*a21*a25 *b69*u *v
81 x
32 2 2 4
- ----*f(v,v )*f(v,v)*a17*a21 *a25 *b1*u *v
81 x
32 2 2 4
+ ----*f(v,v )*f(v,v)*a17*a21 *a25 *b69*u *v
81 x
16 3 6
- ----*f(v,v )*a17*a21 *a25*b1*u *v
81 x
16 3 6 1 4 4 2
+ ----*f(v,v )*a17*a21 *a25*b69*u *v - -----*f(v,v) *a21*a25 *b1*u *v
81 x 243
1 4 4 2 4 3 2 3 4
+ -----*f(v,v) *a21*a25 *b69*u *v - -----*f(v,v) *a21 *a25 *b1*u *v
243 243
4 3 2 3 4 2 2 3 2 6
+ -----*f(v,v) *a21 *a25 *b69*u *v - ----*f(v,v) *a21 *a25 *b1*u *v
243 81
2 2 3 2 6 4 4 8
+ ----*f(v,v) *a21 *a25 *b69*u *v - -----*f(v,v)*a21 *a25*b1*u *v
81 243
4 4 8 1 5 10
+ -----*f(v,v)*a21 *a25*b69*u *v - -----*a21 *b1*u *v
243 243
1 5 10 5
+ -----*a21 *b69*u *v)/a17
243
df(u,t)=(27*df(u,x,3)*a16*a17**4 + df(u,x,3)*a17**2*a25**3 + 27*df(u,x,2)*f(v,v)
*a16*a17**3*a25 + df(u,x,2)*f(v,v)*a17*a25**4 + 27*df(u,x,2)*a16*a17**3*a21*u**2
+ df(u,x,2)*a17*a21*a25**3*u**2 + 81*df(u,x)**2*a16*a17**3*a21*u + 3*df(u,x)**2
*a17*a21*a25**3*u + 54*df(u,x)*f(v,df(v,x))*a16*a17**3*a25 + 2*df(u,x)*f(v,df(v,
x))*a17*a25**4 + 9*df(u,x)*f(v,v)**2*a16*a17**2*a25**2 + 1/3*df(u,x)*f(v,v)**2*
a25**5 + 30*df(u,x)*f(v,v)*a16*a17**2*a21*a25*u**2 + 2/3*df(u,x)*f(v,v)*a21*a25
**4*u**2 + 9*df(u,x)*a16*a17**2*a21**2*u**4 + 1/3*df(u,x)*a21**2*a25**3*u**4 +
18*f(df(v,x),df(v,x))*a16*a17**3*a25*u + f(df(v,x),df(v,x))*a17*a25**4*u + 18*f(
v,df(v,x,2))*a16*a17**3*a25*u + 18*f(v,df(v,x))*f(v,v)*a16*a17**2*a25**2*u + 6*f
(v,df(v,x))*a16*a17**2*a21*a25*u**3 + f(v,v)**3*a16*a17*a25**3*u + 2*f(v,v)**2*
a16*a17*a21*a25**2*u**3 + f(v,v)*a16*a17*a21**2*a25*u**5)/(a17*a25**3)$
df(u,s)=(df(u,x,5)*a17**5*b1 + 5/3*df(u,x,4)*f(v,v)*a17**4*a25*b1 + 5/3*df(u,x,4
)*a17**4*a21*b1*u**2 + 40/3*df(u,x,3)*df(u,x)*a17**4*a21*b1*u + 20/3*df(u,x,3)*f
(v,df(v,x))*a17**4*a25*b1 + 10/9*df(u,x,3)*f(v,v)**2*a17**3*a25**2*b1 + 8/3*df(u
,x,3)*f(v,v)*a17**3*a21*a25*b1*u**2 - 4/9*df(u,x,3)*f(v,v)*a17**3*a21*a25*b69*u
**2 + 10/9*df(u,x,3)*a17**3*a21**2*b1*u**4 + 25/3*df(u,x,2)**2*a17**4*a21*b1*u +
50/3*df(u,x,2)*df(u,x)**2*a17**4*a21*b1 + 44/3*df(u,x,2)*df(u,x)*f(v,v)*a17**3*
a21*a25*b1*u - 4/3*df(u,x,2)*df(u,x)*f(v,v)*a17**3*a21*a25*b69*u + 40/3*df(u,x,2
)*df(u,x)*a17**3*a21**2*b1*u**3 + 20/3*df(u,x,2)*f(df(v,x),df(v,x))*a17**4*a25*
b1 + 20/3*df(u,x,2)*f(v,df(v,x,2))*a17**4*a25*b1 + 20/3*df(u,x,2)*f(v,df(v,x))*f
(v,v)*a17**3*a25**2*b1 + 8*df(u,x,2)*f(v,df(v,x))*a17**3*a21*a25*b1*u**2 - 4/3*
df(u,x,2)*f(v,df(v,x))*a17**3*a21*a25*b69*u**2 + 10/27*df(u,x,2)*f(v,v)**3*a17**
2*a25**3*b1 + 14/9*df(u,x,2)*f(v,v)**2*a17**2*a21*a25**2*b1*u**2 - 4/9*df(u,x,2)
*f(v,v)**2*a17**2*a21*a25**2*b69*u**2 + 14/9*df(u,x,2)*f(v,v)*a17**2*a21**2*a25*
b1*u**4 - 4/9*df(u,x,2)*f(v,v)*a17**2*a21**2*a25*b69*u**4 + 10/27*df(u,x,2)*a17
**2*a21**3*b1*u**6 + 40/9*df(u,x)**3*f(v,v)*a17**3*a21*a25*b1 + 140/9*df(u,x)**3
*a17**3*a21**2*b1*u**2 + 172/9*df(u,x)**2*f(v,df(v,x))*a17**3*a21*a25*b1*u - 4/3
*df(u,x)**2*f(v,df(v,x))*a17**3*a21*a25*b69*u + 82/27*df(u,x)**2*f(v,v)**2*a17**
2*a21*a25**2*b1*u - 4/9*df(u,x)**2*f(v,v)**2*a17**2*a21*a25**2*b69*u + 20/3*df(u
,x)**2*f(v,v)*a17**2*a21**2*a25*b1*u**3 - 40/27*df(u,x)**2*f(v,v)*a17**2*a21**2*
a25*b69*u**3 + 70/27*df(u,x)**2*a17**2*a21**3*b1*u**5 + 10*df(u,x)*f(df(v,x),df(
v,x,2))*a17**4*a25*b1 + 40/9*df(u,x)*f(df(v,x),df(v,x))*f(v,v)*a17**3*a25**2*b1
+ 68/9*df(u,x)*f(df(v,x),df(v,x))*a17**3*a21*a25*b1*u**2 + 4/3*df(u,x)*f(df(v,x)
,df(v,x))*a17**3*a21*a25*b69*u**2 + 10/3*df(u,x)*f(v,df(v,x,3))*a17**4*a25*b1 +
40/9*df(u,x)*f(v,df(v,x,2))*f(v,v)*a17**3*a25**2*b1 + 68/9*df(u,x)*f(v,df(v,x,2)
)*a17**3*a21*a25*b1*u**2 - 28/9*df(u,x)*f(v,df(v,x,2))*a17**3*a21*a25*b69*u**2 +
20/3*df(u,x)*f(v,df(v,x))**2*a17**3*a25**2*b1 + 20/9*df(u,x)*f(v,df(v,x))*f(v,v
)**2*a17**2*a25**3*b1 + 208/27*df(u,x)*f(v,df(v,x))*f(v,v)*a17**2*a21*a25**2*b1*
u**2 - 88/27*df(u,x)*f(v,df(v,x))*f(v,v)*a17**2*a21*a25**2*b69*u**2 + 92/27*df(u
,x)*f(v,df(v,x))*a17**2*a21**2*a25*b1*u**4 - 32/27*df(u,x)*f(v,df(v,x))*a17**2*
a21**2*a25*b69*u**4 + 5/81*df(u,x)*f(v,v)**4*a17*a25**4*b1 + 4/9*df(u,x)*f(v,v)
**3*a17*a21*a25**3*b1*u**2 - 16/81*df(u,x)*f(v,v)**3*a17*a21*a25**3*b69*u**2 +
62/81*df(u,x)*f(v,v)**2*a17*a21**2*a25**2*b1*u**4 - 32/81*df(u,x)*f(v,v)**2*a17*
a21**2*a25**2*b69*u**4 + 4/9*df(u,x)*f(v,v)*a17*a21**3*a25*b1*u**6 - 16/81*df(u,
x)*f(v,v)*a17*a21**3*a25*b69*u**6 + 5/81*df(u,x)*a17*a21**4*b1*u**8 + 2*f(df(v,x
,2),df(v,x,2))*a17**4*a25*b1*u - 1/3*f(df(v,x,2),df(v,x,2))*a17**4*a25*b69*u + 8
/3*f(df(v,x),df(v,x,3))*a17**4*a25*b1*u + 2/3*f(df(v,x),df(v,x,3))*a17**4*a25*
b69*u + 10/3*f(df(v,x),df(v,x,2))*f(v,v)*a17**3*a25**2*b1*u - 10/9*f(df(v,x),df(
v,x,2))*f(v,v)*a17**3*a25**2*b69*u + 2*f(df(v,x),df(v,x,2))*a17**3*a21*a25*b1*u
**3 + 2/9*f(df(v,x),df(v,x,2))*a17**3*a21*a25*b69*u**3 + 40/9*f(df(v,x),df(v,x))
*f(v,df(v,x))*a17**3*a25**2*b1*u + 20/27*f(df(v,x),df(v,x))*f(v,v)**2*a17**2*a25
**3*b1*u - 10/27*f(df(v,x),df(v,x))*f(v,v)**2*a17**2*a25**3*b69*u + 28/27*f(df(v
,x),df(v,x))*f(v,v)*a17**2*a21*a25**2*b1*u**3 - 8/27*f(df(v,x),df(v,x))*f(v,v)*
a17**2*a21*a25**2*b69*u**3 + 8/27*f(df(v,x),df(v,x))*a17**2*a21**2*a25*b1*u**5 +
2/27*f(df(v,x),df(v,x))*a17**2*a21**2*a25*b69*u**5 + 2/3*f(v,df(v,x,4))*a17**4*
a25*b1*u - 2/3*f(v,df(v,x,4))*a17**4*a25*b69*u + 10/9*f(v,df(v,x,3))*f(v,v)*a17
**3*a25**2*b1*u - 10/9*f(v,df(v,x,3))*f(v,v)*a17**3*a25**2*b69*u + 2/3*f(v,df(v,
x,3))*a17**3*a21*a25*b1*u**3 - 2/3*f(v,df(v,x,3))*a17**3*a21*a25*b69*u**3 + 40/9
*f(v,df(v,x,2))*f(v,df(v,x))*a17**3*a25**2*b1*u - 40/9*f(v,df(v,x,2))*f(v,df(v,x
))*a17**3*a25**2*b69*u + 20/27*f(v,df(v,x,2))*f(v,v)**2*a17**2*a25**3*b1*u - 20/
27*f(v,df(v,x,2))*f(v,v)**2*a17**2*a25**3*b69*u + 28/27*f(v,df(v,x,2))*f(v,v)*
a17**2*a21*a25**2*b1*u**3 - 28/27*f(v,df(v,x,2))*f(v,v)*a17**2*a21*a25**2*b69*u
**3 + 8/27*f(v,df(v,x,2))*a17**2*a21**2*a25*b1*u**5 - 8/27*f(v,df(v,x,2))*a17**2
*a21**2*a25*b69*u**5 + 20/9*f(v,df(v,x))**2*f(v,v)*a17**2*a25**3*b1*u - 20/9*f(v
,df(v,x))**2*f(v,v)*a17**2*a25**3*b69*u + 32/27*f(v,df(v,x))**2*a17**2*a21*a25**
2*b1*u**3 - 32/27*f(v,df(v,x))**2*a17**2*a21*a25**2*b69*u**3 + 20/81*f(v,df(v,x)
)*f(v,v)**3*a17*a25**4*b1*u - 20/81*f(v,df(v,x))*f(v,v)**3*a17*a25**4*b69*u + 44
/81*f(v,df(v,x))*f(v,v)**2*a17*a21*a25**3*b1*u**3 - 44/81*f(v,df(v,x))*f(v,v)**2
*a17*a21*a25**3*b69*u**3 + 28/81*f(v,df(v,x))*f(v,v)*a17*a21**2*a25**2*b1*u**5 -
28/81*f(v,df(v,x))*f(v,v)*a17*a21**2*a25**2*b69*u**5 + 4/81*f(v,df(v,x))*a17*
a21**3*a25*b1*u**7 - 4/81*f(v,df(v,x))*a17*a21**3*a25*b69*u**7 + 1/243*f(v,v)**5
*a25**5*b1*u - 1/243*f(v,v)**5*a25**5*b69*u + 4/243*f(v,v)**4*a21*a25**4*b1*u**3
- 4/243*f(v,v)**4*a21*a25**4*b69*u**3 + 2/81*f(v,v)**3*a21**2*a25**3*b1*u**5 -
2/81*f(v,v)**3*a21**2*a25**3*b69*u**5 + 4/243*f(v,v)**2*a21**3*a25**2*b1*u**7 -
4/243*f(v,v)**2*a21**3*a25**2*b69*u**7 + 1/243*f(v,v)*a21**4*a25*b1*u**9 - 1/243
*f(v,v)*a21**4*a25*b69*u**9)/a17**5$
df(v,t)=( - 18*df(u,x,2)*a16*a17**3*a21*u*v + 9*df(u,x)**2*a16*a17**3*a21*v + df
(u,x)**2*a17*a21*a25**3*v + 2*df(u,x)*df(v,x)*a17*a21*a25**3*u - 6*df(u,x)*f(v,v
)*a16*a17**2*a21*a25*u*v - 18*df(u,x)*a16*a17**2*a21**2*u**3*v + df(v,x,3)*a17**
2*a25**3 + df(v,x,2)*f(v,v)*a17*a25**4 + df(v,x,2)*a17*a21*a25**3*u**2 + 2*df(v,
x)*f(v,df(v,x))*a17*a25**4 + 1/3*df(v,x)*f(v,v)**2*a25**5 + 2/3*df(v,x)*f(v,v)*
a21*a25**4*u**2 + 1/3*df(v,x)*a21**2*a25**3*u**4 + f(df(v,x),df(v,x))*a17*a25**4
*v - 12*f(v,df(v,x))*a16*a17**2*a21*a25*u**2*v - f(v,v)**2*a16*a17*a21*a25**2*u
**2*v - 2*f(v,v)*a16*a17*a21**2*a25*u**4*v - a16*a17*a21**3*u**6*v)/(a17*a25**3)
$
df(v,s)=( - 2/3*df(u,x,4)*a17**4*a21*b1*u*v + 2/3*df(u,x,4)*a17**4*a21*b69*u*v +
2/3*df(u,x,3)*df(u,x)*a17**4*a21*b1*v + 8/3*df(u,x,3)*df(u,x)*a17**4*a21*b69*v
+ 10/3*df(u,x,3)*df(v,x)*a17**4*a21*b69*u - 2/3*df(u,x,3)*f(v,v)*a17**3*a21*a25*
b1*u*v + 2/3*df(u,x,3)*f(v,v)*a17**3*a21*a25*b69*u*v - 10/9*df(u,x,3)*a17**3*a21
**2*b1*u**3*v + 10/9*df(u,x,3)*a17**3*a21**2*b69*u**3*v - 1/3*df(u,x,2)**2*a17**
4*a21*b1*v + 2*df(u,x,2)**2*a17**4*a21*b69*v + 10*df(u,x,2)*df(u,x)*df(v,x)*a17
**4*a21*b69 + 2/9*df(u,x,2)*df(u,x)*f(v,v)*a17**3*a21*a25*b1*v + 2*df(u,x,2)*df(
u,x)*f(v,v)*a17**3*a21*a25*b69*v - 50/9*df(u,x,2)*df(u,x)*a17**3*a21**2*b1*u**2*
v + 70/9*df(u,x,2)*df(u,x)*a17**3*a21**2*b69*u**2*v + 20/3*df(u,x,2)*df(v,x,2)*
a17**4*a21*b69*u + 40/9*df(u,x,2)*df(v,x)*f(v,v)*a17**3*a21*a25*b69*u + 40/9*df(
u,x,2)*df(v,x)*a17**3*a21**2*b69*u**3 - 28/9*df(u,x,2)*f(v,df(v,x))*a17**3*a21*
a25*b1*u*v + 28/9*df(u,x,2)*f(v,df(v,x))*a17**3*a21*a25*b69*u*v - 8/27*df(u,x,2)
*f(v,v)**2*a17**2*a21*a25**2*b1*u*v + 8/27*df(u,x,2)*f(v,v)**2*a17**2*a21*a25**2
*b69*u*v - 28/27*df(u,x,2)*f(v,v)*a17**2*a21**2*a25*b1*u**3*v + 28/27*df(u,x,2)*
f(v,v)*a17**2*a21**2*a25*b69*u**3*v - 20/27*df(u,x,2)*a17**2*a21**3*b1*u**5*v +
20/27*df(u,x,2)*a17**2*a21**3*b69*u**5*v + 40/9*df(u,x)**3*a17**3*a21**2*b69*u*v
+ 20/3*df(u,x)**2*df(v,x,2)*a17**4*a21*b69 + 40/9*df(u,x)**2*df(v,x)*f(v,v)*a17
**3*a21*a25*b69 + 100/9*df(u,x)**2*df(v,x)*a17**3*a21**2*b69*u**2 + 4/3*df(u,x)
**2*f(v,df(v,x))*a17**3*a21*a25*b1*v + 28/9*df(u,x)**2*f(v,df(v,x))*a17**3*a21*
a25*b69*v + 2/27*df(u,x)**2*f(v,v)**2*a17**2*a21*a25**2*b1*v + 8/27*df(u,x)**2*f
(v,v)**2*a17**2*a21*a25**2*b69*v - 40/27*df(u,x)**2*f(v,v)*a17**2*a21**2*a25*b1*
u**2*v + 20/9*df(u,x)**2*f(v,v)*a17**2*a21**2*a25*b69*u**2*v - 70/27*df(u,x)**2*
a17**2*a21**3*b1*u**4*v + 80/27*df(u,x)**2*a17**2*a21**3*b69*u**4*v + 20/3*df(u,
x)*df(v,x,3)*a17**4*a21*b69*u + 20/3*df(u,x)*df(v,x,2)*f(v,v)*a17**3*a21*a25*b69
*u + 20/3*df(u,x)*df(v,x,2)*a17**3*a21**2*b69*u**3 + 40/3*df(u,x)*df(v,x)*f(v,df
(v,x))*a17**3*a21*a25*b69*u + 20/9*df(u,x)*df(v,x)*f(v,v)**2*a17**2*a21*a25**2*
b69*u + 40/9*df(u,x)*df(v,x)*f(v,v)*a17**2*a21**2*a25*b69*u**3 + 20/9*df(u,x)*df
(v,x)*a17**2*a21**3*b69*u**5 - 4/3*df(u,x)*f(df(v,x),df(v,x))*a17**3*a21*a25*b1*
u*v + 52/9*df(u,x)*f(df(v,x),df(v,x))*a17**3*a21*a25*b69*u*v - 4/3*df(u,x)*f(v,
df(v,x,2))*a17**3*a21*a25*b1*u*v + 4/3*df(u,x)*f(v,df(v,x,2))*a17**3*a21*a25*b69
*u*v - 32/27*df(u,x)*f(v,df(v,x))*f(v,v)*a17**2*a21*a25**2*b1*u*v + 32/27*df(u,x
)*f(v,df(v,x))*f(v,v)*a17**2*a21*a25**2*b69*u*v - 88/27*df(u,x)*f(v,df(v,x))*a17
**2*a21**2*a25*b1*u**3*v + 88/27*df(u,x)*f(v,df(v,x))*a17**2*a21**2*a25*b69*u**3
*v - 4/81*df(u,x)*f(v,v)**3*a17*a21*a25**3*b1*u*v + 4/81*df(u,x)*f(v,v)**3*a17*
a21*a25**3*b69*u*v - 28/81*df(u,x)*f(v,v)**2*a17*a21**2*a25**2*b1*u**3*v + 28/81
*df(u,x)*f(v,v)**2*a17*a21**2*a25**2*b69*u**3*v - 44/81*df(u,x)*f(v,v)*a17*a21**
3*a25*b1*u**5*v + 44/81*df(u,x)*f(v,v)*a17*a21**3*a25*b69*u**5*v - 20/81*df(u,x)
*a17*a21**4*b1*u**7*v + 20/81*df(u,x)*a17*a21**4*b69*u**7*v + df(v,x,5)*a17**5*
b69 + 5/3*df(v,x,4)*f(v,v)*a17**4*a25*b69 + 5/3*df(v,x,4)*a17**4*a21*b69*u**2 +
20/3*df(v,x,3)*f(v,df(v,x))*a17**4*a25*b69 + 10/9*df(v,x,3)*f(v,v)**2*a17**3*a25
**2*b69 + 20/9*df(v,x,3)*f(v,v)*a17**3*a21*a25*b69*u**2 + 10/9*df(v,x,3)*a17**3*
a21**2*b69*u**4 + 20/3*df(v,x,2)*f(df(v,x),df(v,x))*a17**4*a25*b69 + 20/3*df(v,x
,2)*f(v,df(v,x,2))*a17**4*a25*b69 + 20/3*df(v,x,2)*f(v,df(v,x))*f(v,v)*a17**3*
a25**2*b69 + 20/3*df(v,x,2)*f(v,df(v,x))*a17**3*a21*a25*b69*u**2 + 10/27*df(v,x,
2)*f(v,v)**3*a17**2*a25**3*b69 + 10/9*df(v,x,2)*f(v,v)**2*a17**2*a21*a25**2*b69*
u**2 + 10/9*df(v,x,2)*f(v,v)*a17**2*a21**2*a25*b69*u**4 + 10/27*df(v,x,2)*a17**2
*a21**3*b69*u**6 + 10*df(v,x)*f(df(v,x),df(v,x,2))*a17**4*a25*b69 + 40/9*df(v,x)
*f(df(v,x),df(v,x))*f(v,v)*a17**3*a25**2*b69 + 40/9*df(v,x)*f(df(v,x),df(v,x))*
a17**3*a21*a25*b69*u**2 + 10/3*df(v,x)*f(v,df(v,x,3))*a17**4*a25*b69 + 40/9*df(v
,x)*f(v,df(v,x,2))*f(v,v)*a17**3*a25**2*b69 + 40/9*df(v,x)*f(v,df(v,x,2))*a17**3
*a21*a25*b69*u**2 + 20/3*df(v,x)*f(v,df(v,x))**2*a17**3*a25**2*b69 + 20/9*df(v,x
)*f(v,df(v,x))*f(v,v)**2*a17**2*a25**3*b69 + 40/9*df(v,x)*f(v,df(v,x))*f(v,v)*
a17**2*a21*a25**2*b69*u**2 + 20/9*df(v,x)*f(v,df(v,x))*a17**2*a21**2*a25*b69*u**
4 + 5/81*df(v,x)*f(v,v)**4*a17*a25**4*b69 + 20/81*df(v,x)*f(v,v)**3*a17*a21*a25
**3*b69*u**2 + 10/27*df(v,x)*f(v,v)**2*a17*a21**2*a25**2*b69*u**4 + 20/81*df(v,x
)*f(v,v)*a17*a21**3*a25*b69*u**6 + 5/81*df(v,x)*a17*a21**4*b69*u**8 + 5/3*f(df(v
,x,2),df(v,x,2))*a17**4*a25*b69*v + 10/3*f(df(v,x),df(v,x,3))*a17**4*a25*b69*v +
20/9*f(df(v,x),df(v,x,2))*f(v,v)*a17**3*a25**2*b69*v - 4/3*f(df(v,x),df(v,x,2))
*a17**3*a21*a25*b1*u**2*v + 32/9*f(df(v,x),df(v,x,2))*a17**3*a21*a25*b69*u**2*v
+ 40/9*f(df(v,x),df(v,x))*f(v,df(v,x))*a17**3*a25**2*b69*v + 10/27*f(df(v,x),df(
v,x))*f(v,v)**2*a17**2*a25**3*b69*v - 4/9*f(df(v,x),df(v,x))*f(v,v)*a17**2*a21*
a25**2*b1*u**2*v + 32/27*f(df(v,x),df(v,x))*f(v,v)*a17**2*a21*a25**2*b69*u**2*v
- 4/9*f(df(v,x),df(v,x))*a17**2*a21**2*a25*b1*u**4*v + 22/27*f(df(v,x),df(v,x))*
a17**2*a21**2*a25*b69*u**4*v - 4/9*f(v,df(v,x,3))*a17**3*a21*a25*b1*u**2*v + 4/9
*f(v,df(v,x,3))*a17**3*a21*a25*b69*u**2*v - 4/9*f(v,df(v,x,2))*f(v,v)*a17**2*a21
*a25**2*b1*u**2*v + 4/9*f(v,df(v,x,2))*f(v,v)*a17**2*a21*a25**2*b69*u**2*v - 4/9
*f(v,df(v,x,2))*a17**2*a21**2*a25*b1*u**4*v + 4/9*f(v,df(v,x,2))*a17**2*a21**2*
a25*b69*u**4*v - 28/27*f(v,df(v,x))**2*a17**2*a21*a25**2*b1*u**2*v + 28/27*f(v,
df(v,x))**2*a17**2*a21*a25**2*b69*u**2*v - 16/81*f(v,df(v,x))*f(v,v)**2*a17*a21*
a25**3*b1*u**2*v + 16/81*f(v,df(v,x))*f(v,v)**2*a17*a21*a25**3*b69*u**2*v - 32/
81*f(v,df(v,x))*f(v,v)*a17*a21**2*a25**2*b1*u**4*v + 32/81*f(v,df(v,x))*f(v,v)*
a17*a21**2*a25**2*b69*u**4*v - 16/81*f(v,df(v,x))*a17*a21**3*a25*b1*u**6*v + 16/
81*f(v,df(v,x))*a17*a21**3*a25*b69*u**6*v - 1/243*f(v,v)**4*a21*a25**4*b1*u**2*v
+ 1/243*f(v,v)**4*a21*a25**4*b69*u**2*v - 4/243*f(v,v)**3*a21**2*a25**3*b1*u**4
*v + 4/243*f(v,v)**3*a21**2*a25**3*b69*u**4*v - 2/81*f(v,v)**2*a21**3*a25**2*b1*
u**6*v + 2/81*f(v,v)**2*a21**3*a25**2*b69*u**6*v - 4/243*f(v,v)*a21**4*a25*b1*u
**8*v + 4/243*f(v,v)*a21**4*a25*b69*u**8*v - 1/243*a21**5*b1*u**10*v + 1/243*a21
**5*b69*u**10*v)/a17**5$