Solution 18 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
3 2
---*a7 *b1
8
b39=------------
2
a4
b38=0
3 2
---*a1*a7 *b1
2
b37=---------------
3
a4
b36=0
b35=0
b34=0
a7*b1
b33=-------
a4
1 1
---*a3*a7*b1 - ---*a4*a7*b1
2 2
b32=-----------------------------
2
a4
b31=0
b30=0
3 2 2
---*a1 *a7 *b1
2
b29=----------------
4
a4
b28=0
b27=0
b26=0
a1*a7*b1
b25=----------
2
a4
b24=0
b23=0
3 2
---*a7 *b1
2
b22=------------
a1*a4
2
6*a7 *b1
b21=----------
2
a4
15 2
----*a7 *b1
8
b20=-------------
2
a4
9*a7*b1
b19=---------
a1
5
---*a7*b1
2
b18=-----------
a1
a3*a7*b1 + 6*a4*a7*b1
b17=-----------------------
a1*a4
3
---*a3*a7*b1 + 3*a4*a7*b1
2
b16=---------------------------
a1*a4
2
6*a1*a7 *b1
b15=-------------
3
a4
15 2
----*a1*a7 *b1
2
b14=----------------
3
a4
5*a7*b1
b13=---------
a4
3*a3*a7*b1 + 6*a4*a7*b1
b12=-------------------------
2
a4
10*a7*b1
b11=----------
a4
3 11
---*a3*a7*b1 + ----*a4*a7*b1
2 2
b10=------------------------------
2
a4
9*a7*b1
b9=---------
a4
5
---*a7*b1
2
b8=-----------
a4
a4*b1
b7=-------
a1
a3*b1 + 2*a4*b1
b6=-----------------
a1
3*a3*b1 + a4*b1
b5=-----------------
a1
15 2 2
----*a1 *a7 *b1
2
b4=-----------------
4
a4
10*a1*a7*b1
b3=-------------
2
a4
5*a1*a7*b1
b2=------------
2
a4
a12=0
1
---*a1*a7
2
a11=-----------
a4
2
a1 *a7
a10=--------
2
a4
a9=0
a8=0
2*a1*a7
a6=---------
a4
3
---*a1*a7
2
a5=-----------
a4
2
3*a1 *a7
a2=----------
2
a4
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,a3,a7,a4,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 3 2 2
df(u,t)=(u *a1*a4 + ---*u *f(v,v)*a1*a4*a7 + 3*u *a1 *a7*u + f(v ,v )*a3*a4
3x 2 x x x 2x
3 2 2
+ f(v,v )*a4 + f(v,v )*f(v,v)*a4 *a7 + 2*f(v,v )*a1*a4*a7*u)/a4
3x x x
1 2
---*v *f(v,v)*a1*a4*a7 + v *a1 *a7*u
2 x x
df(v,t)=--------------------------------------
2
a4
4 5 3 2 2
df(u,s)=(u *a1*a4 *b1 + ---*u *f(v,v)*a1*a4 *a7*b1 + 5*u *a1 *a4 *a7*b1*u
5x 2 3x 3x
2 2 3
+ 10*u *u *a1 *a4 *a7*b1 + 9*u *f(v,v )*a1*a4 *a7*b1
2x x 2x x
3 2 11 3
+ ---*u *f(v ,v )*a1*a3*a4 *a7*b1 + ----*u *f(v ,v )*a1*a4 *a7*b1
2 x x x 2 x x x
3 15 2 2 2
+ 10*u *f(v,v )*a1*a4 *a7*b1 + ----*u *f(v,v) *a1*a4 *a7 *b1
x 2x 8 x
15 2 2 15 3 2 2
+ ----*u *f(v,v)*a1 *a4*a7 *b1*u + ----*u *a1 *a7 *b1*u
2 x 2 x
4 5 4
+ 3*f(v ,v )*a3*a4 *b1 + f(v ,v )*a4 *b1 + f(v ,v )*a3*a4 *b1
2x 3x 2x 3x x 4x
5 3 3
+ 2*f(v ,v )*a4 *b1 + ---*f(v ,v )*f(v,v)*a3*a4 *a7*b1
x 4x 2 x 2x
4 2
+ 3*f(v ,v )*f(v,v)*a4 *a7*b1 + 3*f(v ,v )*a1*a3*a4 *a7*b1*u
x 2x x 2x
3 3
+ 6*f(v ,v )*a1*a4 *a7*b1*u + f(v ,v )*f(v,v )*a3*a4 *a7*b1
x 2x x x x
4 5
+ 6*f(v ,v )*f(v,v )*a4 *a7*b1 + f(v,v )*a4 *b1
x x x 5x
5 4 3
+ ---*f(v,v )*f(v,v)*a4 *a7*b1 + 5*f(v,v )*a1*a4 *a7*b1*u
2 3x 3x
4 3 2 3 2
+ 9*f(v,v )*f(v,v )*a4 *a7*b1 + ---*f(v,v )*f(v,v) *a4 *a7 *b1
2x x 2 x
2 2 2 2 2
+ 6*f(v,v )*f(v,v)*a1*a4 *a7 *b1*u + 6*f(v,v )*a1 *a4*a7 *b1*u )/(a1
x x
4
*a4 )
2 1 2
df(v,s)=(u *v *a1*a4 *a7*b1 + ---*v *f(v ,v )*a3*a4 *a7*b1
2x x 2 x x x
1 3 3
- ---*v *f(v ,v )*a4 *a7*b1 + v *f(v,v )*a4 *a7*b1
2 x x x x 2x
3 2 2 2 3 2
+ ---*v *f(v,v) *a4 *a7 *b1 + ---*v *f(v,v)*a1*a4*a7 *b1*u
8 x 2 x
3 2 2 2 4
+ ---*v *a1 *a7 *b1*u )/a4
2 x