Solution 34 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
1 2
---*a10 *b38
4
b42=--------------
2
a18
- a10*b38
b41=------------
a18
3 3
- a10*a17 *b38 + a10*a18 *b7
b40=-------------------------------
2 2
a17 *a18
b39=0
2*a17*b38
b37=-----------
a18
b36=0
2
- a18 *b7
b35=------------
2
a17
- a18*b7
b34=-----------
a17
3 3
a17 *b38 + a18 *b7
b33=--------------------
2
a17*a18
b32=0
b31=0
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
1 3
---*a10 *b38
4
b23=--------------
3
a18
2
- a10 *b38
b22=-------------
2
a18
5 2 3 2 3
- ---*a10 *a17 *b38 + a10 *a18 *b7
2
b21=-------------------------------------
2 3
a17 *a18
a10*b38
b20=---------
a18
6*a10*a17*b38
b19=---------------
2
a18
3 3
a10*a17 *b38 - a10*a18 *b7
b18=----------------------------
2 2
a17 *a18
3 3
2*a10*a17 *b38 - 2*a10*a18 *b7
b17=--------------------------------
3
a17*a18
3 3
a10*a17 *b38 - 2*a10*a18 *b7
b16=------------------------------
3
a17*a18
2
2*a10*a17 *b38
b15=----------------
3
a18
b14=0
- 2*a17*b38
b13=--------------
a18
- 2*a17*b38
b12=--------------
a18
2
- 2*a17 *b38
b11=---------------
2
a18
2
- 2*a17 *b38
b10=---------------
2
a18
3 3
- 2*a17 *b38 + 2*a18 *b7
b9=---------------------------
2
a17*a18
a18*b7
b8=--------
a17
3 3
- 2*a17 *b38 - a18 *b7
b6=-------------------------
3
a18
b5=0
b4=0
b3=0
b2=0
b1=0
1
a19= - ---*a10
2
a16=0
a15=0
a14=0
a13=0
a12=0
1 2
- ---*a10
2
a11=-------------
a18
3*a10*a17
a9=-----------
a18
a8=0
a7= - 2*a17
a6= - a17
2
- a17
a5=---------
a18
2
- a17
a4=---------
a18
a3=0
a2=0
a1=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:
b38,b7,a10,a17,a18
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 2
df(u,t)=( - u *f(v,v)*a17*a18 - f(v ,v )*a17 - f(v,v )*a17
x x x 2x
1 3 2
+ 3*f(v,v )*f(v,v)*a10*a17 - 2*f(v,v )*a17*a18*u - ---*f(v,v) *a10
x x 2
2
+ f(v,v) *a10*a18*u)/a18
1 2
df(v,t)=f(v,v )*a17*v - ---*f(v,v) *a10*v + f(v,v)*a18*u*v
x 2
4 4
df(u,s)=(u *f(v,v)*a17*a18 *b7 - 2*u *f(v,v )*a17 *a18*b38
2x x x
4 2 3
+ 2*u *f(v,v )*a17*a18 *b7 + u *f(v,v) *a10*a17 *a18*b38
x x x
2 4 3 2
- u *f(v,v) *a10*a18 *b7 - 2*u *f(v,v)*a17 *a18 *b38*u
x x
5 2 3
- 2*f(v ,v )*a17 *b38 - f(v ,v )*a17 *a18 *b7
x 2x x 2x
4 4
+ 2*f(v ,v )*f(v,v)*a10*a17 *b38 - 2*f(v ,v )*a17 *a18*b38*u
x x x x
2 3 4
+ f(v,v )*a17 *a18 *b7 + f(v,v )*f(v,v)*a10*a17 *b38
3x 2x
3 4
- 2*f(v,v )*f(v,v)*a10*a17*a18 *b7 - 2*f(v,v )*a17 *a18*b38*u
2x 2x
2 4 2 3
+ 2*f(v,v ) *a10*a17 *b38 - 2*f(v,v ) *a10*a17*a18 *b7
x x
5 2 2 3 2 2 3
- ---*f(v,v )*f(v,v) *a10 *a17 *b38 + f(v,v )*f(v,v) *a10 *a18 *b7
2 x x
3 3 2 2
+ 6*f(v,v )*f(v,v)*a10*a17 *a18*b38*u - 2*f(v,v )*a17 *a18 *b38*u
x x
1 4 3 2 3 2 2
+ ---*f(v,v) *a10 *a17 *b38 - f(v,v) *a10 *a17 *a18*b38*u
4
2 2 2 2 2 3
+ f(v,v) *a10*a17 *a18 *b38*u )/(a17 *a18 )
4 4 3
df(v,s)=( - u *f(v,v)*a18 *b7*v + f(v ,v )*a17 *b38*v + f(v ,v )*a17*a18 *b7*v
x x x x x
3 3
- f(v,v )*a17*a18 *b7*v - f(v,v )*f(v,v)*a10*a17 *b38*v
2x x
3 3
+ f(v,v )*f(v,v)*a10*a18 *b7*v + 2*f(v,v )*a17 *a18*b38*u*v
x x
1 3 2 2 2 2
+ ---*f(v,v) *a10 *a17 *b38*v - f(v,v) *a10*a17 *a18*b38*u*v
4
2 2 2 2 2
+ f(v,v)*a17 *a18 *b38*u *v)/(a17 *a18 )