Solution 2 to problem l1o24
Expressions |
Parameters |
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Back to problem l1o24
Expressions
The solution is given through the following expressions:
b39=0
3 3
----*a4*a8 *b1
16
b38=----------------
4
a6
3 2
---*a4*a8 *b1
4
b37=---------------
3
a6
b36=0
3 2
---*a4*a8 *b1
4
b35=---------------
3
a6
3
---*a4*a8*b1
2
b34=--------------
2
a6
3
- ---*a4*a8*b1
4
b33=-----------------
2
a6
b32=0
b31=0
17 4
- ----*a8 *b1
16
b30=----------------
4
a6
9 3
- ---*a8 *b1
2
b29=---------------
3
a6
39 3
- ----*a8 *b1
4
b28=----------------
3
a6
27 2
- ----*a8 *b1
2
b27=----------------
2
a6
2
- 27*a8 *b1
b26=--------------
2
a6
33 2
- ----*a8 *b1
4
b25=----------------
2
a6
2
- 11*a8 *b1
b24=--------------
2
a6
- 18*a8*b1
b23=-------------
a6
- 27*a8*b1
b22=-------------
a6
- 18*a8*b1
b21=-------------
a6
- 5*a8*b1
b20=------------
a6
b19= - 9*b1
b18=0
b17=0
b16=0
3 2
- ---*a4*a8 *b1
4
b15=------------------
3
a6
3 2
- ---*a4*a8 *b1
4
b14=------------------
3
a6
3
- ---*a4*a8*b1
2
b13=-----------------
2
a6
3
- ---*a4*a8*b1
2
b12=-----------------
2
a6
9
- ---*a4*a8*b1
2
b11=-----------------
2
a6
3
- ---*a4*a8*b1
2
b10=-----------------
2
a6
- 3*a4*b1
b9=------------
a6
b8=0
b7=0
3
4*a8 *b1
b6=----------
3
a6
2
12*a8 *b1
b5=-----------
2
a6
2
6*a8 *b1
b4=----------
2
a6
10*a8*b1
b3=----------
a6
4*a8*b1
b2=---------
a6
1
- ---*a4*a8
4
a10=--------------
a6
17 2
----*a8
12
a9=----------
a6
5
a7=---*a8
3
a5=0
a3=0
14
a2= - ----*a8
3
7
a1= - ---*a6
3
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,a4,a8,a6
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
7 14
df(u,t)= - ---*u *a6 - ----*u *a8*u + f(v,v )*a4
3 2x 3 x x
3 2 2
df(u,s)=(u *a6 *b1 + 4*u *a6 *a8*b1*u + 10*u *u *a6 *a8*b1
4x 3x 2x x
3 2 2 2 2
- ---*u *f(v,v)*a4*a6*a8*b1 + 6*u *a6*a8 *b1*u + 12*u *a6*a8 *b1*u
2 2x 2x x
9 3 2
- ---*u *f(v,v )*a4*a6*a8*b1 - ---*u *f(v,v)*a4*a8 *b1*u
2 x x 4 x
3 3 3 2
+ 4*u *a8 *b1*u - ---*f(v ,v )*a4*a6*a8*b1*u - 3*f(v,v )*a4*a6 *b1
x 2 x x 3x
3 3 2 2 3
- ---*f(v,v )*a4*a6*a8*b1*u - ---*f(v,v )*a4*a8 *b1*u )/a6
2 2x 4 x
df(v,t)=
5 2 1 17 2 2
---*u *a6*a8*v + v *a6 + v *a6*a8*u - ---*f(v,v)*a4*a8*v + ----*a8 *u *v
3 x 2x x 4 12
----------------------------------------------------------------------------
a6
3 3 2 2
df(v,s)=( - 5*u *a6 *a8*b1*v - 18*u *v *a6 *a8*b1 - 11*u *a6 *a8 *b1*u*v
3x 2x x 2x
33 2 2 2 3 2 2
- ----*u *a6 *a8 *b1*v - 27*u *v *a6 *a8*b1 - 27*u *v *a6 *a8 *b1*u
4 x x 2x x x
3 2 39 3 2 4
+ ---*u *f(v,v)*a4*a6*a8 *b1*v - ----*u *a6*a8 *b1*u *v - 9*v *a6 *b1
4 x 4 x 4x
3 27 2 2 2 9 3 3
- 18*v *a6 *a8*b1*u - ----*v *a6 *a8 *b1*u - ---*v *a6*a8 *b1*u
3x 2 2x 2 x
3 2 3 2
- ---*f(v ,v )*a4*a6 *a8*b1*v + ---*f(v,v )*a4*a6 *a8*b1*v
4 x x 2 2x
3 2 3 3 2
+ ---*f(v,v )*a4*a6*a8 *b1*u*v + ----*f(v,v)*a4*a8 *b1*u *v
4 x 16
17 4 4 4
- ----*a8 *b1*u *v)/a6
16
df(u,t)= - 7/3*df(u,x,2)*a6 - 14/3*df(u,x)*a8*u + f(v,df(v,x))*a4$
df(u,s)=(df(u,x,4)*a6**3*b1 + 4*df(u,x,3)*a6**2*a8*b1*u + 10*df(u,x,2)*df(u,x)*
a6**2*a8*b1 - 3/2*df(u,x,2)*f(v,v)*a4*a6*a8*b1 + 6*df(u,x,2)*a6*a8**2*b1*u**2 +
12*df(u,x)**2*a6*a8**2*b1*u - 9/2*df(u,x)*f(v,df(v,x))*a4*a6*a8*b1 - 3/4*df(u,x)
*f(v,v)*a4*a8**2*b1*u + 4*df(u,x)*a8**3*b1*u**3 - 3/2*f(df(v,x),df(v,x))*a4*a6*
a8*b1*u - 3*f(v,df(v,x,3))*a4*a6**2*b1 - 3/2*f(v,df(v,x,2))*a4*a6*a8*b1*u - 3/4*
f(v,df(v,x))*a4*a8**2*b1*u**2)/a6**3$
df(v,t)=(5/3*df(u,x)*a6*a8*v + df(v,x,2)*a6**2 + df(v,x)*a6*a8*u - 1/4*f(v,v)*a4
*a8*v + 17/12*a8**2*u**2*v)/a6$
df(v,s)=( - 5*df(u,x,3)*a6**3*a8*b1*v - 18*df(u,x,2)*df(v,x)*a6**3*a8*b1 - 11*df
(u,x,2)*a6**2*a8**2*b1*u*v - 33/4*df(u,x)**2*a6**2*a8**2*b1*v - 27*df(u,x)*df(v,
x,2)*a6**3*a8*b1 - 27*df(u,x)*df(v,x)*a6**2*a8**2*b1*u + 3/4*df(u,x)*f(v,v)*a4*
a6*a8**2*b1*v - 39/4*df(u,x)*a6*a8**3*b1*u**2*v - 9*df(v,x,4)*a6**4*b1 - 18*df(v
,x,3)*a6**3*a8*b1*u - 27/2*df(v,x,2)*a6**2*a8**2*b1*u**2 - 9/2*df(v,x)*a6*a8**3*
b1*u**3 - 3/4*f(df(v,x),df(v,x))*a4*a6**2*a8*b1*v + 3/2*f(v,df(v,x,2))*a4*a6**2*
a8*b1*v + 3/4*f(v,df(v,x))*a4*a6*a8**2*b1*u*v + 3/16*f(v,v)*a4*a8**3*b1*u**2*v -
17/16*a8**4*b1*u**4*v)/a6**4$