Solution 1 to problem l2313o35
Expressions |
Parameters |
Relevance |
Back to problem l2313o35
Expressions
The solution is given through the following expressions:
b126=0
b125=0
b124=0
b123=0
b122=0
b121=0
b120=0
b119=0
b118=0
b117=0
b116=0
b115=0
1
- ---*a19*a3*b1
3
b114=------------------
2
a1
1
- ----*a19*a3*b1
12
b113=-------------------
2
a1
1
- ---*a19*a3*b1
3
b112=------------------
2
a1
1
- ---*a19*a3*b1
4
b111=------------------
2
a1
b110=0
1
---*a19*a3*b1
3
b109=---------------
2
a1
1
---*a19*a3*b1
3
b108=---------------
2
a1
b107=0
b106=0
b105=0
b104=0
b103=0
b102=0
b101=0
b100=0
b99=0
b98=0
b97=0
b96=0
b95=0
b94=0
b93=0
b92=0
b91=0
b90=0
b89=0
- a19*b1
b88=-----------
a1
a19*b1
b87=--------
a1
1
- ---*a19*b1
4
b86=---------------
a1
b85=0
b84=0
b83=0
b82=0
b81=0
b80=0
b79=0
b78=0
b77=0
b76=0
b75=0
b74=0
b73=0
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=0
b63=0
b62=0
b61=0
b60=0
b59=0
b58=0
b57=0
b56=0
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
1 2
----*a19*a3 *b1
36
b47=-----------------
3
a1
b46=0
1 2
----*a19*a3 *b1
12
b45=-----------------
3
a1
b44=0
b43=0
b42=0
b41=0
b40=0
b39=0
b38=0
b37=0
b36=0
b35=0
b34=0
1
----*a19*a3*b1
12
b33=----------------
2
a1
b32=0
b31=0
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=0
b22=0
b21=0
b20=0
b19=0
b18=0
b17=0
b16=0
b15=0
b14=0
b13=0
b12=0
b11=0
b10=0
b9=0
1
---*a3*b1
3
b8=-----------
a1
5
---*a3*b1
3
b7=-----------
a1
10
----*a3*b1
3
b6=------------
a1
b5=0
b4=0
b3=0
b2=0
1
- ---*a19*a3
4
a22=---------------
a1
1
---*a19*a3
6
a21=------------
a1
a20= - a19
1
a18= - ---*a19
4
a17=0
a16=0
a15=0
a14=0
a13=0
a12=0
1 2
----*a19*a3
36
a11=--------------
2
a1
a10=0
1
----*a19*a3
12
a9=-------------
a1
a8=0
a7=0
a6=0
a5=0
1
a4=---*a3
3
a2=0
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:
b1,a19,a3,a1
Relevance for the application:
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3 1 3 2
df(u,t)=(u *a1 + ----*u *f(v,v) *a1*a19*a3 + f(v ,v )*a1 *a3
3x 12 x x 2x
1 2 1 3 2 2
+ ---*f(v,v )*a1 *a3 + ----*f(v,v )*f(v,v) *a19*a3 )/a1
3 3x 36 x
1 2 1 3
df(v,t)=( - ---*u *f(v,v) *a1*a19*v + ---*v *f(v,v) *a19*a3
4 x 6 x
2 1 2
+ v *f(v,v) *a1*a19*u - ---*f(v,v )*f(v,v) *a19*a3*v
x 4 x
- f(v,v )*f(v,v)*a1*a19*u*v)/a1
x
3 1 3 10 2
df(u,s)=(u *a1 *b1 + ----*u *f(v,v) *a1*a19*a3*b1 + ----*f(v ,v )*a1 *a3*b1
5x 12 3x 3 2x 3x
5 2 1 3 2
+ ---*f(v ,v )*a1 *a3*b1 + ----*f(v ,v )*f(v,v) *a19*a3 *b1
3 x 4x 12 x 2x
1 2 1 3 2 3
+ ---*f(v,v )*a1 *a3*b1 + ----*f(v,v )*f(v,v) *a19*a3 *b1)/a1
3 5x 36 3x
1 2 2
df(v,s)=( - ---*u *f(v,v) *a1*a19*b1*v + u *v *f(v,v) *a1*a19*b1
4 3x 2x x
1 2
- u *f(v,v )*f(v,v)*a1*a19*b1*v + ---*v *f(v ,v )*f(v,v) *a19*a3*b1
2x x 3 x x x
1 2
+ ---*v *f(v,v )*f(v,v) *a19*a3*b1
3 x 2x
1 2
- ---*f(v ,v )*f(v,v) *a19*a3*b1*v
4 x 2x
1
- ---*f(v ,v )*f(v,v )*f(v,v)*a19*a3*b1*v
3 x x x
1 2
- ----*f(v,v )*f(v,v) *a19*a3*b1*v
12 3x
1 2
- ---*f(v,v )*f(v,v )*f(v,v)*a19*a3*b1*v)/a1
3 2x x