Solution 3 to problem l1o23
Expressions |
Parameters |
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Back to problem l1o23
Expressions
The solution is given through the following expressions:
b21=0
a4*a7*b1
b20=----------
2
a1
a4*a7*b1
b19=----------
2
a1
b18=0
2
4*a7 *b1
b17=----------
2
a1
2
4*a7 *b1
b16=----------
2
a1
b15=0
2*a7*b1
b14=---------
a1
a7*b1
b13=-------
a1
b12=0
b11=0
b10=0
4*a4*a7*b1
b9=------------
2
a1
2*a4*a7*b1
b8=------------
2
a1
a4*b1
b7=-------
a1
a4*b1
b6=-------
a1
b5=0
2
12*a7 *b1
b4=-----------
2
a1
6*a7*b1
b3=---------
a1
6*a7*b1
b2=---------
a1
a10=0
a9=0
a8=2*a7
a6=0
a5=0
a3=0
a2=4*a7
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,a7,a4,a1
Relevance for the application:
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df(u,t)=u *a1 + 4*u *a7*u + f(v,v )*a4
2x x x
df(v,t)=u *a7*v + 2*v *a7*u
x x
2 2
df(u,s)=(u *a1 *b1 + 6*u *a1*a7*b1*u + 6*u *a1*a7*b1 + 2*u *f(v,v)*a4*a7*b1
3x 2x x x
2 2
+ 12*u *a7 *b1*u + f(v ,v )*a1*a4*b1 + f(v,v )*a1*a4*b1
x x x 2x
2
+ 4*f(v,v )*a4*a7*b1*u)/a1
x
2
df(v,s)=(u *a1*a7*b1*v + 2*u *v *a1*a7*b1 + 4*u *a7 *b1*u*v
2x x x x
2 2 2
+ v *f(v,v)*a4*a7*b1 + 4*v *a7 *b1*u + f(v,v )*a4*a7*b1*v)/a1
x x x