Solution 14 to problem l112o13
Expressions |
Parameters |
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Back to problem l112o13
Expressions
The solution is given through the following expressions:
1
b42=---*b22
4
b41=0
1
b40=b18 + ---*b19 - b39
4
b38=0
b37= - b12
b36=0
1
b35=---*b12
4
1
b34=---*b11 - b31 + b8
4
1
b33=---*b10 + b8
4
b32=2*b8 + b9
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b20=0
b14=0
b13= - 4*b12
b5=0
b4=0
b3=0
b2=0
b1=0
a8=0
a7=0
a4=0
a3=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, b22, b21, b19, b18, b17, b16, b15, b12,
b11, b10, b9, b8, b6, b7, a5
Relevance for the application:
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2
df(u,t)=u *a6 + f(v,v) *a5
x
df(v,t)=v *a6
x
2
df(u,s)=u *f(v,v)*b8 + u *f(v,v )*b9 + u *f(v,v) *b18 + u *f(v,v)*b12*u
2x x x x x
+ f(v ,v )*b6 + f(v ,v )*f(v,v)*b15 + f(v ,v )*b10*u + f(v,v )*b7
x 2x x x x x 3x
2 2
+ f(v,v )*f(v,v)*b16 + f(v,v )*b11*u + f(v,v ) *b17 + f(v,v )*f(v,v) *b21
2x 2x x x
2 4 3
+ f(v,v )*f(v,v)*b19*u - 4*f(v,v )*b12*u + f(v,v) *b23 + f(v,v) *b22*u
x x
1
df(v,s)=---*u *f(v,v)*b12*v + v *f(v,v)*b31 + 2*v *f(v,v )*b8 + v *f(v,v )*b9
4 x 2x x x x x
2 1 1
+ v *f(v,v) *b39 + ---*f(v ,v )*b10*v + f(v ,v )*b8*v + ---*f(v,v )*b11*v
x 4 x x x x 4 2x
- f(v,v )*b31*v + f(v,v )*b8*v + f(v,v )*f(v,v)*b18*v
2x 2x x
1
+ ---*f(v,v )*f(v,v)*b19*v - f(v,v )*f(v,v)*b39*v - f(v,v )*b12*u*v
4 x x x
1 3
+ ---*f(v,v) *b22*v
4