Solution 17 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
1
- ---*a11*a2*b1
4
b42=------------------
2
a1
2 3 1 4
4*a1 *a18 *b1 - ----*a11*a2 *b1
32
b41=---------------------------------
3
a1 *a18*a2
2
24*a18 *b1
b40=------------
2
a2
b39=0
3
---*a18*a2*b1
4
b38=---------------
2
a1
3*a18*b1
b37=----------
a1
b36=0
3
---*a18*b1
2
b35=------------
a1
2*a18*b1
b34=----------
a2
2*a18*b1
b33=----------
a2
b32=0
b31=0
1 3
----*a2 *b1
32
b30=-------------
3
a1
b29=0
3 2
----*a2 *b1
16
b28=-------------
2
a1
b27=0
b26=0
1
---*a2*b1
8
b25=-----------
a1
b24=0
4*a11*a18*b1
b23=--------------
a1*a2
2 3 1 4
- 64*a1 *a18 *b1 + ---*a11*a2 *b1
2
b22=------------------------------------
2 3
a1 *a2
3
384*a1*a18 *b1
b21=----------------
4
a2
2
- 12*a18 *b1
b20=---------------
a1*a2
2
144*a18 *b1
b19=-------------
2
a2
2
24*a18 *b1
b18=------------
2
a2
2
384*a1*a18 *b1
b17=----------------
3
a2
2
160*a1*a18 *b1
b16=----------------
3
a2
2
160*a1*a18 *b1
b15=----------------
3
a2
1
- ---*a18*a2*b1
2
b14=------------------
2
a1
12*a18*b1
b13=-----------
a1
9*a18*b1
b12=----------
a1
24*a18*b1
b11=-----------
a2
24*a18*b1
b10=-----------
a2
48*a18*b1
b9=-----------
a2
10*a18*b1
b8=-----------
a2
16*a1*a18*b1
b7=--------------
2
a2
48*a1*a18*b1
b6=--------------
2
a2
b5=0
3 2
---*a2 *b1
4
b4=------------
2
a1
3
---*a2*b1
2
b3=-----------
a1
3
---*a2*b1
2
b2=-----------
a1
1 2
- ----*a11*a2
16
a19=-----------------
a1*a18
2*a1*a18
a17=----------
a2
a16=0
1 2
----*a2
16
a15=----------
a1
a14=0
1
a13=---*a2
8
a12=0
2
- 16*a1*a18
a10=---------------
2
a2
2 2
96*a1 *a18
a9=-------------
3
a2
a8= - a18
16*a1*a18
a7=-----------
a2
6*a1*a18
a6=----------
a2
2
16*a1 *a18
a5=------------
2
a2
2
16*a1 *a18
a4=------------
2
a2
a3=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:
b1,a11,a2,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 4 2
df(u,t)=(u *a1*a2 + 6*u *f(v,v)*a1*a18*a2 + u *a2 *u + 16*f(v ,v )*a1 *a18*a2
2x x x x x
2 2 2
+ 16*f(v,v )*a1 *a18*a2 + 96*f(v,v )*f(v,v)*a1 *a18
2x x
2 3 3 2 2
+ 16*f(v,v )*a1*a18*a2 *u + f(v,v) *a11*a2 - 16*f(v,v) *a1*a18 *a2*u
x
3 2 3
- f(v,v)*a18*a2 *u )/a2
1 2 2 2 1 2 3
df(v,t)=(---*u *a1*a18*a2 *v + 2*f(v,v )*a1 *a18 *v - ----*f(v,v) *a11*a2 *v
8 x x 16
2 1 3 2
+ f(v,v)*a1*a18 *a2*u*v + ----*a18*a2 *u *v)/(a1*a18*a2)
16
2 4 2 3 3 5
df(u,s)=(u *a1 *a2 *b1 + 10*u *f(v,v)*a1 *a18*a2 *b1 + ---*u *a1*a2 *b1*u
3x 2x 2 2x
3 2 5 2 3
+ ---*u *a1*a2 *b1 + 48*u *f(v,v )*a1 *a18*a2 *b1
2 x x x
2 2 2 2 4
+ 24*u *f(v,v) *a1 *a18 *a2 *b1 + 9*u *f(v,v)*a1*a18*a2 *b1*u
x x
3 6 2 3 2
+ ---*u *a2 *b1*u + 48*f(v ,v )*a1 *a18*a2 *b1
4 x x 2x
3 2 2 3
+ 160*f(v ,v )*f(v,v)*a1 *a18 *a2*b1 + 24*f(v ,v )*a1 *a18*a2 *b1*u
x x x x
3 2 3 2
+ 16*f(v,v )*a1 *a18*a2 *b1 + 160*f(v,v )*f(v,v)*a1 *a18 *a2*b1
3x 2x
2 3 2 3 2
+ 24*f(v,v )*a1 *a18*a2 *b1*u + 384*f(v,v ) *a1 *a18 *a2*b1
2x x
2 3 3
+ 384*f(v,v )*f(v,v) *a1 *a18 *b1
x
2 2 2 4 2
+ 144*f(v,v )*f(v,v)*a1 *a18 *a2 *b1*u + 12*f(v,v )*a1*a18*a2 *b1*u
x x
4 3 3 2 3
+ 4*f(v,v) *a1*a11*a18*a2 *b1 - 64*f(v,v) *a1 *a18 *a2*b1*u
1 3 5 2 2 3 2
+ ---*f(v,v) *a11*a2 *b1*u - 12*f(v,v) *a1*a18 *a2 *b1*u
2
1 5 3 2 4
- ---*f(v,v)*a18*a2 *b1*u )/(a1 *a2 )
2
1 2 3 3 2 2 2
df(v,s)=(---*u *a1 *a18*a2 *b1*v + ---*u *f(v,v)*a1 *a18 *a2 *b1*v
8 2x 2 x
3 4 3 2
+ ----*u *a1*a18*a2 *b1*u*v + 2*f(v ,v )*a1 *a18 *a2*b1*v
16 x x x
3 2 3 3
+ 2*f(v,v )*a1 *a18 *a2*b1*v + 24*f(v,v )*f(v,v)*a1 *a18 *b1*v
2x x
2 2 2 1 3 3
+ 3*f(v,v )*a1 *a18 *a2 *b1*u*v - ---*f(v,v) *a1*a11*a18*a2 *b1*v
x 4
2 2 3 1 2 5
+ 4*f(v,v) *a1 *a18 *a2*b1*u*v - ----*f(v,v) *a11*a2 *b1*u*v
32
3 2 3 2 1 5 3 3 2
+ ---*f(v,v)*a1*a18 *a2 *b1*u *v + ----*a18*a2 *b1*u *v)/(a1 *a18*a2 )
4 32