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