Solution 21 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
b39=0
b38=0
b37=0
b36=0
b35=0
b34=0
b33=0
1
---*a10*a3*b1
2
b32=---------------
2
a1
b31=0
b30=0
3 2
---*a10 *b1
2
b29=-------------
2
a1
b28=0
b27=0
b26=0
a10*b1
b25=--------
a1
b24=0
b23=0
b22=0
b21=0
b20=0
b19=0
b18=0
b17=0
b16=0
b15=0
b14=0
b13=0
3*a10*a3*b1
b12=-------------
2
a1
b11=0
3
---*a10*a3*b1
2
b10=---------------
2
a1
b9=0
b8=0
b7=0
a3*b1
b6=-------
a1
3*a3*b1
b5=---------
a1
15 2
----*a10 *b1
2
b4=--------------
2
a1
10*a10*b1
b3=-----------
a1
5*a10*b1
b2=----------
a1
a12=0
a11=0
a9=0
a8=0
a7=0
a6=0
a5=0
a4=0
a2=3*a10
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,a3,a10,a1
Relevance for the application:
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df(u,t)=u *a1 + 3*u *a10*u + f(v ,v )*a3
3x x x 2x
df(v,t)=v *a10*u
x
2
df(u,s)=(u *a1 *b1 + 5*u *a1*a10*b1*u + 10*u *u *a1*a10*b1
5x 3x 2x x
3 15 2 2
+ ---*u *f(v ,v )*a10*a3*b1 + ----*u *a10 *b1*u
2 x x x 2 x
+ 3*f(v ,v )*a1*a3*b1 + f(v ,v )*a1*a3*b1 + 3*f(v ,v )*a10*a3*b1*u
2x 3x x 4x x 2x
2
)/a1
1 3 2 2
u *v *a1*a10*b1 + ---*v *f(v ,v )*a10*a3*b1 + ---*v *a10 *b1*u
2x x 2 x x x 2 x
df(v,s)=------------------------------------------------------------------
2
a1