Solution 26 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
b42=0
b41=0
3 2
a13*a9*b1 + ---*a16 *b1
4
b40=-------------------------
2
a1
3 2
a13*a9*b1 + ---*a16 *b1
4
b39=-------------------------
2
a1
b38=0
4*a13*a16*b1
b37=--------------
2
a1
8*a13*a16*b1
b36=--------------
2
a1
2*a13*a16*b1
b35=--------------
2
a1
1
---*a16*b1
2
b34=------------
a1
1
---*a16*b1
2
b33=------------
a1
2*a16*b1
b32=----------
a1
b31=0
b30=0
2
16*a13 *b1
b29=------------
2
a1
2
8*a13 *b1
b28=-----------
2
a1
b27=0
4*a13*b1
b26=----------
a1
a13*b1
b25=--------
a1
b24=0
b23=0
b22=0
2*a16*a9*b1
b21=-------------
2
a1
b20=0
2
8*a13*a9*b1 + 4*a16 *b1
b19=-------------------------
2
a1
3 2
2*a13*a9*b1 + ---*a16 *b1
2
b18=---------------------------
2
a1
3 2
2*a13*a9*b1 + ---*a16 *b1
2
b17=---------------------------
a1*a13
2
a13*a9*b1 + a16 *b1
b16=---------------------
a1*a13
2
a13*a9*b1 + a16 *b1
b15=---------------------
a1*a13
b14=0
16*a13*a16*b1
b13=---------------
2
a1
20*a13*a16*b1
b12=---------------
2
a1
6*a16*b1
b11=----------
a1
6*a16*b1
b10=----------
a1
10*a16*b1
b9=-----------
a1
5
---*a16*b1
2
b8=------------
a1
1
---*a16*b1
2
b7=------------
a13
3
---*a16*b1
2
b6=------------
a13
b5=0
2
48*a13 *b1
b4=------------
2
a1
12*a13*b1
b3=-----------
a1
12*a13*b1
b2=-----------
a1
a19=0
a18=0
1
a17=---*a16
2
a15=0
a14=4*a13
a12=0
a11=0
a10=0
a8=0
a7=2*a16
3
a6=---*a16
2
1
---*a1*a16
2
a5=------------
a13
1
---*a1*a16
2
a4=------------
a13
a3=0
a2=8*a13
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,a16,a9,a13,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 1
df(u,t)=(u *a1*a13 + ---*u *f(v,v)*a13*a16 + 8*u *a13 *u + ---*f(v ,v )*a1*a16
2x 2 x x 2 x x
1
+ ---*f(v,v )*a1*a16 + f(v,v )*f(v,v)*a13*a9 + 2*f(v,v )*a13*a16*u)/
2 2x x x
a13
1
df(v,t)=u *a13*v + v *f(v,v)*a16 + 4*v *a13*u + ---*f(v,v )*a16*v
x x x 2 x
2 5 2
df(u,s)=(u *a1 *a13*b1 + ---*u *f(v,v)*a1*a13*a16*b1 + 12*u *a1*a13 *b1*u
3x 2 2x 2x
2 2
+ 12*u *a1*a13 *b1 + 10*u *f(v,v )*a1*a13*a16*b1
x x x
2 2 3 2 2
+ 2*u *f(v,v) *a13 *a9*b1 + ---*u *f(v,v) *a13*a16 *b1
x 2 x
2 3 2
+ 20*u *f(v,v)*a13 *a16*b1*u + 48*u *a13 *b1*u
x x
3 2
+ ---*f(v ,v )*a1 *a16*b1 + f(v ,v )*f(v,v)*a1*a13*a9*b1
2 x 2x x x
2
+ f(v ,v )*f(v,v)*a1*a16 *b1 + 6*f(v ,v )*a1*a13*a16*b1*u
x x x x
1 2
+ ---*f(v,v )*a1 *a16*b1 + f(v,v )*f(v,v)*a1*a13*a9*b1
2 3x 2x
2
+ f(v,v )*f(v,v)*a1*a16 *b1 + 6*f(v,v )*a1*a13*a16*b1*u
2x 2x
2 3 2 2
+ 2*f(v,v ) *a1*a13*a9*b1 + ---*f(v,v ) *a1*a16 *b1
x 2 x
2 2
+ 2*f(v,v )*f(v,v) *a13*a16*a9*b1 + 8*f(v,v )*f(v,v)*a13 *a9*b1*u
x x
2 2 2 2
+ 4*f(v,v )*f(v,v)*a13*a16 *b1*u + 16*f(v,v )*a13 *a16*b1*u )/(a1 *a13
x x
)
df(v,s)=(u *a1*a13*b1*v + 4*u *v *a1*a13*b1 + 2*u *f(v,v)*a13*a16*b1*v
2x x x x
2 2
+ 8*u *a13 *b1*u*v + 2*v *f(v,v )*a1*a16*b1 + v *f(v,v) *a13*a9*b1
x x x x
3 2 2 2 2
+ ---*v *f(v,v) *a16 *b1 + 8*v *f(v,v)*a13*a16*b1*u + 16*v *a13 *b1*u
4 x x x
1 1
+ ---*f(v ,v )*a1*a16*b1*v + ---*f(v,v )*a1*a16*b1*v
2 x x 2 2x
3 2
+ f(v,v )*f(v,v)*a13*a9*b1*v + ---*f(v,v )*f(v,v)*a16 *b1*v
x 4 x
2
+ 4*f(v,v )*a13*a16*b1*u*v)/a1
x