Solution 11 to problem l112o13
Expressions |
Parameters |
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Back to problem l112o13
Expressions
The solution is given through the following expressions:
1 2 2 1 2
a3*a5*b18 + ---*a5 *b10 - 3*a5 *b8 - ---*a5 *b9
2 2
b42=-------------------------------------------------
2
a3
b41=0
a3*b18 - a3*b39 + a5*b10
b40=--------------------------
a3
b38=0
b37=0
b36=0
b35=0
b34= - b31 + b8
b33=b8
1 1
b32=---*b10 - b8 + ---*b9
2 2
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
2 2 2
4*a3*a5*b18 + 2*a5 *b10 - 12*a5 *b8 - 2*a5 *b9
b22=------------------------------------------------
2
a3
b20=0
4*a3*b18 + 6*a5*b10 - 12*a5*b8 - 2*a5*b9
b19=------------------------------------------
a3
b14=0
b13=0
b12=0
b11=b10
b5=0
b4=0
b3=0
b2=0
b1=0
a8=0
a7=0
a4=0
a2=0
a0=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:
b39, b31, b23, b21, b18, b17, b16, b15, b10, b9, b8,
b6, b7, a5, a3
Relevance for the application:
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2
df(u,t)=u *a6 + f(v,v )*a3 + f(v,v) *a5
x x
df(v,t)=v *a6
x
2 2 2 2
df(u,s)=(u *f(v,v)*a3 *b8 + u *f(v,v )*a3 *b9 + u *f(v,v) *a3 *b18
2x x x x
2 2 2
+ f(v ,v )*a3 *b6 + f(v ,v )*f(v,v)*a3 *b15 + f(v ,v )*a3 *b10*u
x 2x x x x x
2 2 2
+ f(v,v )*a3 *b7 + f(v,v )*f(v,v)*a3 *b16 + f(v,v )*a3 *b10*u
3x 2x 2x
2 2 2 2
+ f(v,v ) *a3 *b17 + f(v,v )*f(v,v) *a3 *b21
x x
2
+ 4*f(v,v )*f(v,v)*a3 *b18*u + 6*f(v,v )*f(v,v)*a3*a5*b10*u
x x
- 12*f(v,v )*f(v,v)*a3*a5*b8*u - 2*f(v,v )*f(v,v)*a3*a5*b9*u
x x
4 2 3 3 2
+ f(v,v) *a3 *b23 + 4*f(v,v) *a3*a5*b18*u + 2*f(v,v) *a5 *b10*u
3 2 3 2 2
- 12*f(v,v) *a5 *b8*u - 2*f(v,v) *a5 *b9*u)/a3
2 1 2 2
df(v,s)=(v *f(v,v)*a3 *b31 + ---*v *f(v,v )*a3 *b10 - v *f(v,v )*a3 *b8
2x 2 x x x x
1 2 2 2 2
+ ---*v *f(v,v )*a3 *b9 + v *f(v,v) *a3 *b39 + f(v ,v )*a3 *b8*v
2 x x x x x
2 2 2
- f(v,v )*a3 *b31*v + f(v,v )*a3 *b8*v + f(v,v )*f(v,v)*a3 *b18*v
2x 2x x
2
- f(v,v )*f(v,v)*a3 *b39*v + f(v,v )*f(v,v)*a3*a5*b10*v
x x
3 1 3 2 3 2
+ f(v,v) *a3*a5*b18*v + ---*f(v,v) *a5 *b10*v - 3*f(v,v) *a5 *b8*v
2
1 3 2 2
- ---*f(v,v) *a5 *b9*v)/a3
2