Solution 15 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
- ---*a3*a5 *b8 + a5 *a8*b6
2
b42=------------------------------
3
a3
2
2*a3*a5*a8*b8 - 4*a5*a8 *b6
b41=-----------------------------
3
a3
- 3*a3*a5*b8 + 2*a5*a8*b6
b40=----------------------------
2
a3
b39=0
2 3
- 2*a3*a8 *b8 + 4*a8 *b6
b38=---------------------------
3
a3
2
2*a3*a8*b8 - 4*a8 *b6
b37=-----------------------
2
a3
b36=0
2*a8*b8
b35=---------
a3
b34= - b8
1
---*a3*b8 + a8*b6
2
b33=-------------------
a3
b32=0
b31=0
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
1 3 3
- ---*a3*a5 *b8 + a5 *a8*b6
2
b23=------------------------------
3
a3 *a8
2 2
2*a3*a5 *b8 - 4*a5 *a8*b6
b22=---------------------------
3
a3
9 2 2
- ---*a3*a5 *b8 + 5*a5 *a8*b6
2
b21=--------------------------------
2
a3 *a8
2
- 2*a3*a5*a8*b8 + 4*a5*a8 *b6
b20=--------------------------------
3
a3
6*a3*a5*b8 - 12*a5*a8*b6
b19=--------------------------
2
a3
3*a3*a5*b8 - 2*a5*a8*b6
b18=-------------------------
2
a3
- 3*a3*a5*b8 + 2*a5*a8*b6
b17=----------------------------
a3*a8
5
- ---*a3*a5*b8 + a5*a8*b6
2
b16=----------------------------
a3*a8
- a3*a5*b8 + 2*a5*a8*b6
b15=--------------------------
a3*a8
b14=0
2
- 2*a3*a8*b8 + 4*a8 *b6
b13=--------------------------
2
a3
2
- 2*a3*a8*b8 + 4*a8 *b6
b12=--------------------------
2
a3
a3*b8 - 2*a8*b6
b11=-----------------
a3
a3*b8 - 2*a8*b6
b10=-----------------
a3
3*a3*b8 - 2*a8*b6
b9=-------------------
a3
1
- ---*a3*b8
2
b7=--------------
a8
b5=0
b4=0
b3=0
b2=0
b1=0
a7=0
a4=0
a2=0
a1=a6
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:
b6, b8, a6, a5, a8, a3
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(u,t)=u *a6 + f(v,v )*a3 + f(v,v) *a5
x x
df(v,t)=v *a6 + f(v,v)*a8*v
x
3 3
df(u,s)=(u *f(v,v)*a3 *a8*b8 + 3*u *f(v,v )*a3 *a8*b8
2x x x
2 2 2 2
- 2*u *f(v,v )*a3 *a8 *b6 + 3*u *f(v,v) *a3 *a5*a8*b8
x x x
2 2 2 2
- 2*u *f(v,v) *a3*a5*a8 *b6 - 2*u *f(v,v)*a3 *a8 *b8*u
x x
3 3
+ 4*u *f(v,v)*a3*a8 *b6*u + f(v ,v )*a3 *a8*b6
x x 2x
3 2
- f(v ,v )*f(v,v)*a3 *a5*b8 + 2*f(v ,v )*f(v,v)*a3 *a5*a8*b6
x x x x
3 2 2
+ f(v ,v )*a3 *a8*b8*u - 2*f(v ,v )*a3 *a8 *b6*u
x x x x
1 4 5 3
- ---*f(v,v )*a3 *b8 - ---*f(v,v )*f(v,v)*a3 *a5*b8
2 3x 2 2x
2 3
+ f(v,v )*f(v,v)*a3 *a5*a8*b6 + f(v,v )*a3 *a8*b8*u
2x 2x
2 2 2 3
- 2*f(v,v )*a3 *a8 *b6*u - 3*f(v,v ) *a3 *a5*b8
2x x
2 2 9 2 2 2
+ 2*f(v,v ) *a3 *a5*a8*b6 - ---*f(v,v )*f(v,v) *a3 *a5 *b8
x 2 x
2 2 2
+ 5*f(v,v )*f(v,v) *a3*a5 *a8*b6 + 6*f(v,v )*f(v,v)*a3 *a5*a8*b8*u
x x
2 2 2 2
- 12*f(v,v )*f(v,v)*a3*a5*a8 *b6*u - 2*f(v,v )*a3 *a8 *b8*u
x x
3 2 1 4 3 4 3
+ 4*f(v,v )*a3*a8 *b6*u - ---*f(v,v) *a3*a5 *b8 + f(v,v) *a5 *a8*b6
x 2
3 2 3 2 2
+ 2*f(v,v) *a3*a5 *a8*b8*u - 4*f(v,v) *a5 *a8 *b6*u
2 2 2 2 3 2 3
- 2*f(v,v) *a3*a5*a8 *b8*u + 4*f(v,v) *a5*a8 *b6*u )/(a3 *a8)
2 1 3 2
df(v,s)=(2*u *f(v,v)*a3 *a8*b8*v + ---*f(v ,v )*a3 *b8*v + f(v ,v )*a3 *a8*b6*v
x 2 x x x x
3 2
- f(v,v )*a3 *b8*v - 3*f(v,v )*f(v,v)*a3 *a5*b8*v
2x x
2
+ 2*f(v,v )*f(v,v)*a3*a5*a8*b6*v + 2*f(v,v )*a3 *a8*b8*u*v
x x
2 1 3 2
- 4*f(v,v )*a3*a8 *b6*u*v - ---*f(v,v) *a3*a5 *b8*v
x 2
3 2 2
+ f(v,v) *a5 *a8*b6*v + 2*f(v,v) *a3*a5*a8*b8*u*v
2 2 2 2
- 4*f(v,v) *a5*a8 *b6*u*v - 2*f(v,v)*a3*a8 *b8*u *v
3 2 3
+ 4*f(v,v)*a8 *b6*u *v)/a3