Solution 19 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
4 2 5 2 2 15 2 4
a1 *a7 *b1 - ---*a1 *a10*a4 *a7*b1 + ----*a10 *a4 *b1
2 8
b39=-------------------------------------------------------
4 2
a1 *a4
b38=0
2 5 2 2
- a1 *a10*a7*b1 + ---*a10 *a4 *b1
2
b37=------------------------------------
3
a1 *a4
b36=0
b35=0
b34=0
a10*a4*b1
b33=-----------
2
a1
a10*a4*b1
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
2 2 5 2
- a1 *a7 *b1 + ---*a10*a4 *a7*b1
2
b22=-----------------------------------
3
a1 *a4
2 2 2
a1 *a10*a7*b1 + 5*a10 *a4 *b1
b21=-------------------------------
4
a1
15 2 2
----*a10 *a4 *b1
8
b20=------------------
4
a1
2
9*a10*a4 *b1
b19=--------------
3
a1
5 2
---*a10*a4 *b1
2
b18=----------------
3
a1
2
9*a10*a4 *b1
b17=--------------
3
a1
15 2
----*a10*a4 *b1
2
b16=-----------------
3
a1
2
6*a10 *a4*b1
b15=--------------
3
a1
15 2
----*a10 *a4*b1
2
b14=-----------------
3
a1
5*a10*a4*b1
b13=-------------
2
a1
15*a10*a4*b1
b12=--------------
2
a1
10*a10*a4*b1
b11=--------------
2
a1
10*a10*a4*b1
b10=--------------
2
a1
9*a10*a4*b1
b9=-------------
2
a1
5
---*a10*a4*b1
2
b8=---------------
2
a1
a4*b1
b7=-------
a1
5*a4*b1
b6=---------
a1
10*a4*b1
b5=----------
a1
15 2
----*a10 *b1
2
b4=--------------
2
a1
10*a10*b1
b3=-----------
a1
5*a10*b1
b2=----------
a1
a12=0
2 3 2
- a1 *a7 + ---*a10*a4
2
a11=-------------------------
a1*a4
a9=0
a8=0
2*a10*a4
a6=----------
a1
3
---*a10*a4
2
a5=------------
a1
a3=3*a4
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,a7,a4,a10,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 3
df(u,t)=(u *a1 + ---*u *f(v,v)*a10*a4 + 3*u *a1*a10*u + 3*f(v ,v )*a1*a4
3x 2 x x x 2x
+ f(v,v )*a1*a4 + f(v,v )*f(v,v)*a1*a7 + 2*f(v,v )*a10*a4*u)/a1
3x x x
2 3 2
- v *f(v,v)*a1 *a7 + ---*v *f(v,v)*a10*a4 + v *a1*a10*a4*u
x 2 x x
df(v,t)=--------------------------------------------------------------
a1*a4
4 5 2 2 3
df(u,s)=(u *a1 *a4*b1 + ---*u *f(v,v)*a1 *a10*a4 *b1 + 5*u *a1 *a10*a4*b1*u
5x 2 3x 3x
3 2 2
+ 10*u *u *a1 *a10*a4*b1 + 9*u *f(v,v )*a1 *a10*a4 *b1
2x x 2x x
2 2 2 2
+ 10*u *f(v ,v )*a1 *a10*a4 *b1 + 10*u *f(v,v )*a1 *a10*a4 *b1
x x x x 2x
15 2 2 3 15 2 2
+ ----*u *f(v,v) *a10 *a4 *b1 + ----*u *f(v,v)*a1*a10 *a4 *b1*u
8 x 2 x
15 2 2 2 3 2
+ ----*u *a1 *a10 *a4*b1*u + 10*f(v ,v )*a1 *a4 *b1
2 x 2x 3x
3 2 15 3
+ 5*f(v ,v )*a1 *a4 *b1 + ----*f(v ,v )*f(v,v)*a1*a10*a4 *b1
x 4x 2 x 2x
2 2 3
+ 15*f(v ,v )*a1 *a10*a4 *b1*u + 9*f(v ,v )*f(v,v )*a1*a10*a4 *b1
x 2x x x x
3 2 5 3
+ f(v,v )*a1 *a4 *b1 + ---*f(v,v )*f(v,v)*a1*a10*a4 *b1
5x 2 3x
2 2 3
+ 5*f(v,v )*a1 *a10*a4 *b1*u + 9*f(v,v )*f(v,v )*a1*a10*a4 *b1
3x 2x x
2 3 2 5 2 2
- f(v,v )*f(v,v) *a1 *a7 *b1 + ---*f(v,v )*f(v,v) *a1*a10*a4 *a7*b1
x 2 x
2 2 3
+ f(v,v )*f(v,v)*a1 *a10*a4*a7*b1*u + 5*f(v,v )*f(v,v)*a10 *a4 *b1*u
x x
2 2 2 4
+ 6*f(v,v )*a1*a10 *a4 *b1*u )/(a1 *a4)
x
3 2 2 3
df(v,s)=(u *v *a1 *a10*a4 *b1 + v *f(v ,v )*a1 *a10*a4 *b1
2x x x x x
2 3 2 4 2
+ v *f(v,v )*a1 *a10*a4 *b1 + v *f(v,v) *a1 *a7 *b1
x 2x x
5 2 2 2 15 2 2 4
- ---*v *f(v,v) *a1 *a10*a4 *a7*b1 + ----*v *f(v,v) *a10 *a4 *b1
2 x 8 x
3 5 2 3
- v *f(v,v)*a1 *a10*a4*a7*b1*u + ---*v *f(v,v)*a1*a10 *a4 *b1*u
x 2 x
3 2 2 2 2 4 2
+ ---*v *a1 *a10 *a4 *b1*u )/(a1 *a4 )
2 x