Solution 1 to problem l112o12
Expressions |
Parameters |
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Back to problem l112o12
Expressions
The solution is given through the following expressions:
1 2 1 2 1 2
- ---*a0*a4 *b13 + ---*a0*a4 *b2 + ---*a4 *a7*b1
4 8 4
b19=---------------------------------------------------
2
a0 *a7
1
a0*a4*b13 - ---*a0*a4*b2 - a4*a7*b1
2
b18=-------------------------------------
2
a0
- a4*b13
b17=-----------
a7
- a0*a4*b13 + a4*a7*b1
b16=-------------------------
a0*a7
2*a0*b13 - 2*a7*b1
b14=--------------------
a0
- a0*b13 + a7*b1
b12=-------------------
a7
1 3 1 3 1 3
- ---*a0*a4 *b13 + ---*a0*a4 *b2 + ---*a4 *a7*b1
4 8 4
b11=---------------------------------------------------
2 2
a0 *a7
2 1 2 2
a0*a4 *b13 - ---*a0*a4 *b2 - a4 *a7*b1
2
b10=----------------------------------------
2
a0 *a7
2 1 2 2
- 2*a0*a4 *b13 + ---*a0*a4 *b2 + a4 *a7*b1
2
b9=---------------------------------------------
2
a0*a7
1
- a0*a4*b13 + ---*a0*a4*b2 + a4*a7*b1
2
b8=----------------------------------------
2
a0
2*a0*a4*b13 - a0*a4*b2 - 2*a4*a7*b1
b7=-------------------------------------
a0*a7
1
a4*b13 - ---*a4*b2
2
b6=--------------------
a7
- a0*a4*b13
b5=--------------
2
a7
- a4*b1
b4=----------
a7
b3=0
1
a8= - ---*a4
2
1 2
- ---*a4
2
a5=------------
a7
a2=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:
b15, a3, b13, b1, b2, a4, a0, a7
Relevance for the application:
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df(u,t)=
1 2 2
u *a0*a7 + u *a6*a7 + f(v,v )*a3*a7 - ---*f(v,v) *a4 + f(v,v)*a4*a7*u
x x x 2
------------------------------------------------------------------------
a7
1
df(v,t)=v *a6 - ---*f(v,v)*a4*v + a7*u*v
x 2
2 2 2 1 2
df(u,s)=(u *a0 *a7 *b1 + u *f(v,v)*a0 *a4*a7*b13 - ---*u *f(v,v)*a0 *a4*a7*b2
2x x 2 x
2 2 2 3
+ u *a0 *a7 *b2*u - f(v ,v )*a0 *a4*a7*b1 - f(v,v )*a0 *a4*b13
x x x 2x
2 2 1 2 2
- 2*f(v,v )*f(v,v)*a0 *a4 *b13 + ---*f(v,v )*f(v,v)*a0 *a4 *b2
x 2 x
2 2
+ f(v,v )*f(v,v)*a0*a4 *a7*b1 + 2*f(v,v )*a0 *a4*a7*b13*u
x x
2 2
- f(v,v )*a0 *a4*a7*b2*u - 2*f(v,v )*a0*a4*a7 *b1*u
x x
1 3 3 1 3 3
- ---*f(v,v) *a0*a4 *b13 + ---*f(v,v) *a0*a4 *b2
4 8
1 3 3 2 2
+ ---*f(v,v) *a4 *a7*b1 + f(v,v) *a0*a4 *a7*b13*u
4
1 2 2 2 2 2
- ---*f(v,v) *a0*a4 *a7*b2*u - f(v,v) *a4 *a7 *b1*u
2
2 2 1 2 2
- f(v,v)*a0*a4*a7 *b13*u + ---*f(v,v)*a0*a4*a7 *b2*u
2
3 2 2 2
+ f(v,v)*a4*a7 *b1*u )/(a0 *a7 )
2 3 2 2
df(v,s)=(u *a0 *a7*b13*v - v *a0 *b13 + v *a0 *a7*b1 - v *f(v,v)*a0 *a4*b13
x 2x 2x x
2 2
+ v *f(v,v)*a0*a4*a7*b1 + 2*v *a0 *a7*b13*u - 2*v *a0*a7 *b1*u
x x x
2 1 2 2
- f(v,v )*a0 *a4*b13*v - ---*f(v,v) *a0*a4 *b13*v
x 4
1 2 2 1 2 2
+ ---*f(v,v) *a0*a4 *b2*v + ---*f(v,v) *a4 *a7*b1*v
8 4
1
+ f(v,v)*a0*a4*a7*b13*u*v - ---*f(v,v)*a0*a4*a7*b2*u*v
2
2 2 2 2
- f(v,v)*a4*a7 *b1*u*v + a0 *a7*b15*u *v)/(a0 *a7)