Solution 15 to problem l1o35
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Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=(3*a14**2*a7**2*b2)/a2**4
b72=0
b71=(8*a14**3*a7*b2)/a2**4
b70=(16*a14**3*a7*b2)/a2**4
b69=(12*a14**3*a7*b2)/a2**4
b68=(6*a14**2*a7*b2)/a2**3
b67=(6*a14**2*a7*b2)/a2**3
b66=(12*a14**2*a7*b2)/a2**3
b65=0
b64=(8*a14**2*a7*b2)/a2**3
b63=(10*a14**2*a7*b2)/a2**3
b62=(3*a14**2*a7*b2)/a2**3
b61=(a14*a7*b2)/a2**2
b60=(3*a14*a7*b2)/a2**2
b59=(2*a14*a7*b2)/a2**2
b58=(2*a14*a7*b2)/a2**2
b57=0
b56=0
b55=0
b54=(16*a14**4*b2)/a2**4
b53=(32*a14**4*b2)/a2**4
b52=0
b51=(48*a14**3*b2)/a2**3
b50=(48*a14**3*b2)/a2**3
b49=(24*a14**3*b2)/a2**3
b48=0
b47=0
b46=(12*a14**2*b2)/a2**2
b45=(16*a14**2*b2)/a2**2
b44=(20*a14**2*b2)/a2**2
b43=(8*a14**2*b2)/a2**2
b42=0
b41=0
b40=0
b39=(2*a14*b2)/a2
b38=(a14*b2)/a2
b37=0
b36=0
b35=0
b34=(12*a14**2*a7**2*b2)/a2**4
b33=(3*a14**2*a7**2*b2)/a2**4
b32=(6*a14*a7**2*b2)/a2**3
b31=(3*a14*a7**2*b2)/a2**3
b30=(3*a14*a7**2*b2)/a2**3
b29=0
b28=(32*a14**3*a7*b2)/a2**4
b27=(48*a14**3*a7*b2)/a2**4
b26=(24*a14**2*a7*b2)/a2**3
b25=(24*a14**2*a7*b2)/a2**3
b24=(96*a14**2*a7*b2)/a2**3
b23=(24*a14**2*a7*b2)/a2**3
b22=(24*a14**2*a7*b2)/a2**3
b21=(8*a14*a7*b2)/a2**2
b20=(24*a14*a7*b2)/a2**2
b19=(20*a14*a7*b2)/a2**2
b18=(20*a14*a7*b2)/a2**2
b17=(20*a14*a7*b2)/a2**2
b16=(4*a14*a7*b2)/a2**2
b15=(a7*b2)/a2
b14=(4*a7*b2)/a2
b13=(3*a7*b2)/a2
b12=0
b11=(80*a14**4*b2)/a2**4
b10=(240*a14**3*b2)/a2**3
b9=(80*a14**3*b2)/a2**3
b8=(60*a14**2*b2)/a2**2
b7=(200*a14**2*b2)/a2**2
b6=(40*a14**2*b2)/a2**2
b5=(20*a14*b2)/a2
b4=(30*a14*b2)/a2
b3=(10*a14*b2)/a2
a22=0
a21=0
a20=(2*a14*a7)/a2
a19=0
a18=(4*a14**2)/a2
a17=(4*a14**2)/a2
a16=0
a15=2*a14
a13=0
a12=0
a11=0
a10=(4*a14*a7)/a2
a9=(2*a14*a7)/a2
a8=a7
a6=0
a5=(12*a14**2)/a2
a4=6*a14
a3=6*a14
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:
b2,a14,a7,a2
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2 2
df(u,t)=(u *a2 + 6*u *a14*a2*u + 6*u *a14*a2 + 2*u *f(v,v)*a14*a7
3x 2x x x
2 2
+ 12*u *a14 *u + f(v ,v )*a2*a7 + f(v,v )*a2*a7 + 4*f(v,v )*a14*a7*u
x x x 2x x
)/a2
2
df(v,t)=(u *a14*a2*v + 2*u *v *a14*a2 + 4*u *a14 *u*v + 2*v *f(v,v)*a14*a7
2x x x x x
2 2
+ 4*v *a14 *u )/a2
x
4 3 3
df(u,s)=(u *a2 *b2 + 10*u *a14*a2 *b2*u + 30*u *u *a14*a2 *b2
5x 4x 3x x
2 2 2 2
+ 4*u *f(v,v)*a14*a2 *a7*b2 + 40*u *a14 *a2 *b2*u
3x 3x
2 3 2 2
+ 20*u *a14*a2 *b2 + 200*u *u *a14 *a2 *b2*u
2x 2x x
2 2
+ 20*u *f(v,v )*a14*a2 *a7*b2 + 24*u *f(v,v)*a14 *a2*a7*b2*u
2x x 2x
3 3 3 2 2
+ 80*u *a14 *a2*b2*u + 60*u *a14 *a2 *b2
2x x
2 2 2 3 2
+ 24*u *f(v,v)*a14 *a2*a7*b2 + 240*u *a14 *a2*b2*u
x x
2 2
+ 20*u *f(v ,v )*a14*a2 *a7*b2 + 20*u *f(v,v )*a14*a2 *a7*b2
x x x x 2x
2 2 2 2
+ 96*u *f(v,v )*a14 *a2*a7*b2*u + 3*u *f(v,v) *a14 *a7 *b2
x x x
3 2 4 4
+ 48*u *f(v,v)*a14 *a7*b2*u + 80*u *a14 *b2*u
x x
3 3
+ 3*f(v ,v )*a2 *a7*b2 + 4*f(v ,v )*a2 *a7*b2
2x 2x x 3x
2 2
+ 24*f(v ,v )*a14*a2 *a7*b2*u + 3*f(v ,v )*f(v,v)*a14*a2*a7 *b2
x 2x x x
2 2 3
+ 24*f(v ,v )*a14 *a2*a7*b2*u + f(v,v )*a2 *a7*b2
x x 4x
2 2
+ 8*f(v,v )*a14*a2 *a7*b2*u + 3*f(v,v )*f(v,v)*a14*a2*a7 *b2
3x 2x
2 2 2 2
+ 24*f(v,v )*a14 *a2*a7*b2*u + 6*f(v,v ) *a14*a2*a7 *b2
2x x
2 2 3 3 4
+ 12*f(v,v )*f(v,v)*a14 *a7 *b2*u + 32*f(v,v )*a14 *a7*b2*u )/a2
x x
3 3 2 2
df(v,s)=(u *a14*a2 *b2*v + 2*u *v *a14*a2 *b2 + 8*u *a14 *a2 *b2*u*v
4x 3x x 3x
2 2 2 2
+ 20*u *u *a14 *a2 *b2*v + 16*u *v *a14 *a2 *b2*u
2x x 2x x
2 3 2
+ 3*u *f(v,v)*a14 *a2*a7*b2*v + 24*u *a14 *a2*b2*u *v
2x 2x
2 2 2 2 3
+ 12*u *v *a14 *a2 *b2 + 48*u *a14 *a2*b2*u*v
x x x
2 3 2
+ 10*u *v *f(v,v)*a14 *a2*a7*b2 + 48*u *v *a14 *a2*b2*u
x x x x
2 3
+ 8*u *f(v,v )*a14 *a2*a7*b2*v + 12*u *f(v,v)*a14 *a7*b2*u*v
x x x
4 3 2
+ 32*u *a14 *b2*u *v + 2*v *f(v ,v )*a14*a2 *a7*b2
x x x x
2 2
+ 2*v *f(v,v )*a14*a2 *a7*b2 + 12*v *f(v,v )*a14 *a2*a7*b2*u
x 2x x x
2 2 2 3 2
+ 3*v *f(v,v) *a14 *a7 *b2 + 16*v *f(v,v)*a14 *a7*b2*u
x x
4 4 2
+ 16*v *a14 *b2*u + 3*f(v ,v )*a14*a2 *a7*b2*v
x x 2x
2 2
+ 6*f(v ,v )*a14 *a2*a7*b2*u*v + f(v,v )*a14*a2 *a7*b2*v
x x 3x
2 3 2 4
+ 6*f(v,v )*a14 *a2*a7*b2*u*v + 8*f(v,v )*a14 *a7*b2*u *v)/a2
2x x
df(u,t)=(df(u,x,3)*a2**2 + 6*df(u,x,2)*a14*a2*u + 6*df(u,x)**2*a14*a2 + 2*df(u,x
)*f(v,v)*a14*a7 + 12*df(u,x)*a14**2*u**2 + f(df(v,x),df(v,x))*a2*a7 + f(v,df(v,x
,2))*a2*a7 + 4*f(v,df(v,x))*a14*a7*u)/a2$
df(v,t)=(df(u,x,2)*a14*a2*v + 2*df(u,x)*df(v,x)*a14*a2 + 4*df(u,x)*a14**2*u*v +
2*df(v,x)*f(v,v)*a14*a7 + 4*df(v,x)*a14**2*u**2)/a2$
df(u,s)=(df(u,x,5)*a2**4*b2 + 10*df(u,x,4)*a14*a2**3*b2*u + 30*df(u,x,3)*df(u,x)
*a14*a2**3*b2 + 4*df(u,x,3)*f(v,v)*a14*a2**2*a7*b2 + 40*df(u,x,3)*a14**2*a2**2*
b2*u**2 + 20*df(u,x,2)**2*a14*a2**3*b2 + 200*df(u,x,2)*df(u,x)*a14**2*a2**2*b2*u
+ 20*df(u,x,2)*f(v,df(v,x))*a14*a2**2*a7*b2 + 24*df(u,x,2)*f(v,v)*a14**2*a2*a7*
b2*u + 80*df(u,x,2)*a14**3*a2*b2*u**3 + 60*df(u,x)**3*a14**2*a2**2*b2 + 24*df(u,
x)**2*f(v,v)*a14**2*a2*a7*b2 + 240*df(u,x)**2*a14**3*a2*b2*u**2 + 20*df(u,x)*f(
df(v,x),df(v,x))*a14*a2**2*a7*b2 + 20*df(u,x)*f(v,df(v,x,2))*a14*a2**2*a7*b2 +
96*df(u,x)*f(v,df(v,x))*a14**2*a2*a7*b2*u + 3*df(u,x)*f(v,v)**2*a14**2*a7**2*b2
+ 48*df(u,x)*f(v,v)*a14**3*a7*b2*u**2 + 80*df(u,x)*a14**4*b2*u**4 + 3*f(df(v,x,2
),df(v,x,2))*a2**3*a7*b2 + 4*f(df(v,x),df(v,x,3))*a2**3*a7*b2 + 24*f(df(v,x),df(
v,x,2))*a14*a2**2*a7*b2*u + 3*f(df(v,x),df(v,x))*f(v,v)*a14*a2*a7**2*b2 + 24*f(
df(v,x),df(v,x))*a14**2*a2*a7*b2*u**2 + f(v,df(v,x,4))*a2**3*a7*b2 + 8*f(v,df(v,
x,3))*a14*a2**2*a7*b2*u + 3*f(v,df(v,x,2))*f(v,v)*a14*a2*a7**2*b2 + 24*f(v,df(v,
x,2))*a14**2*a2*a7*b2*u**2 + 6*f(v,df(v,x))**2*a14*a2*a7**2*b2 + 12*f(v,df(v,x))
*f(v,v)*a14**2*a7**2*b2*u + 32*f(v,df(v,x))*a14**3*a7*b2*u**3)/a2**4$
df(v,s)=(df(u,x,4)*a14*a2**3*b2*v + 2*df(u,x,3)*df(v,x)*a14*a2**3*b2 + 8*df(u,x,
3)*a14**2*a2**2*b2*u*v + 20*df(u,x,2)*df(u,x)*a14**2*a2**2*b2*v + 16*df(u,x,2)*
df(v,x)*a14**2*a2**2*b2*u + 3*df(u,x,2)*f(v,v)*a14**2*a2*a7*b2*v + 24*df(u,x,2)*
a14**3*a2*b2*u**2*v + 12*df(u,x)**2*df(v,x)*a14**2*a2**2*b2 + 48*df(u,x)**2*a14
**3*a2*b2*u*v + 10*df(u,x)*df(v,x)*f(v,v)*a14**2*a2*a7*b2 + 48*df(u,x)*df(v,x)*
a14**3*a2*b2*u**2 + 8*df(u,x)*f(v,df(v,x))*a14**2*a2*a7*b2*v + 12*df(u,x)*f(v,v)
*a14**3*a7*b2*u*v + 32*df(u,x)*a14**4*b2*u**3*v + 2*df(v,x)*f(df(v,x),df(v,x))*
a14*a2**2*a7*b2 + 2*df(v,x)*f(v,df(v,x,2))*a14*a2**2*a7*b2 + 12*df(v,x)*f(v,df(v
,x))*a14**2*a2*a7*b2*u + 3*df(v,x)*f(v,v)**2*a14**2*a7**2*b2 + 16*df(v,x)*f(v,v)
*a14**3*a7*b2*u**2 + 16*df(v,x)*a14**4*b2*u**4 + 3*f(df(v,x),df(v,x,2))*a14*a2**
2*a7*b2*v + 6*f(df(v,x),df(v,x))*a14**2*a2*a7*b2*u*v + f(v,df(v,x,3))*a14*a2**2*
a7*b2*v + 6*f(v,df(v,x,2))*a14**2*a2*a7*b2*u*v + 8*f(v,df(v,x))*a14**3*a7*b2*u**
2*v)/a2**4$