Solution 5 to problem l1o35
Expressions |
Parameters |
Relevance |
Back to problem l1o35
Expressions
The solution is given through the following expressions:
b75=0
b74=(2*a14**2*a7**2*b2)/a2**4
b73=(a14**2*a7**2*b2)/a2**4
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=(6*a14**2*a7*b2)/a2**3
b63=(6*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=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
b47=0
b46=(6*a14**2*b2)/a2**2
b45=0
b44=(6*a14**2*b2)/a2**2
b43=0
b42=0
b41=0
b40=0
b39=(2*a14*b2)/a2
b38=(a14*b2)/a2
b37=0
b36=0
b35=0
b34=0
b33=(3*a14**2*a7**2*b2)/a2**4
b32=(3*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=0
b27=0
b26=0
b25=0
b24=0
b23=(12*a14**2*a7*b2)/a2**3
b22=0
b21=0
b20=0
b19=(10*a14*a7*b2)/a2**2
b18=(10*a14*a7*b2)/a2**2
b17=(10*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=0
b10=0
b9=0
b8=(10*a14**2*b2)/a2**2
b7=0
b6=0
b5=(5*a14*b2)/a2
b4=(10*a14*b2)/a2
b3=0
a22=0
a21=(a14*a7)/a2
a20=(a14*a7)/a2
a19=0
a18=0
a17=0
a16=0
a15=2*a14
a13=0
a12=0
a11=0
a10=0
a9=(2*a14*a7)/a2
a8=a7
a6=0
a5=0
a4=3*a14
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:
b2,a7,a14,a2
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
df(u,t)=
2 2
u *a2 + 3*u *a14*a2 + 2*u *f(v,v)*a14*a7 + f(v ,v )*a2*a7 + f(v,v )*a2*a7
3x x x x x 2x
-------------------------------------------------------------------------------
a2
u *a14*a2*v + 2*u *v *a14*a2 + v *f(v,v)*a14*a7 + f(v,v )*a14*a7*v
2x x x x x
df(v,t)=---------------------------------------------------------------------
a2
4 3 2
df(u,s)=(u *a2 *b2 + 10*u *u *a14*a2 *b2 + 4*u *f(v,v)*a14*a2 *a7*b2
5x 3x x 3x
2 3 2
+ 5*u *a14*a2 *b2 + 10*u *f(v,v )*a14*a2 *a7*b2
2x 2x x
3 2 2 2 2
+ 10*u *a14 *a2 *b2 + 12*u *f(v,v)*a14 *a2*a7*b2
x x
2 2
+ 10*u *f(v ,v )*a14*a2 *a7*b2 + 10*u *f(v,v )*a14*a2 *a7*b2
x x x x 2x
2 2 2 3
+ 3*u *f(v,v) *a14 *a7 *b2 + 3*f(v ,v )*a2 *a7*b2
x 2x 2x
3 2
+ 4*f(v ,v )*a2 *a7*b2 + 3*f(v ,v )*f(v,v)*a14*a2*a7 *b2
x 3x x x
3 2
+ f(v,v )*a2 *a7*b2 + 3*f(v,v )*f(v,v)*a14*a2*a7 *b2
4x 2x
2 2 4
+ 3*f(v,v ) *a14*a2*a7 *b2)/a2
x
3 3 2 2
df(v,s)=(u *a14*a2 *b2*v + 2*u *v *a14*a2 *b2 + 6*u *u *a14 *a2 *b2*v
4x 3x x 2x x
2 2 2 2
+ 3*u *f(v,v)*a14 *a2*a7*b2*v + 6*u *v *a14 *a2 *b2
2x x x
2 2
+ 6*u *v *f(v,v)*a14 *a2*a7*b2 + 6*u *f(v,v )*a14 *a2*a7*b2*v
x x x x
2 2
+ 2*v *f(v ,v )*a14*a2 *a7*b2 + 2*v *f(v,v )*a14*a2 *a7*b2
x x x x 2x
2 2 2 2
+ v *f(v,v) *a14 *a7 *b2 + 3*f(v ,v )*a14*a2 *a7*b2*v
x x 2x
2 2 2 4
+ f(v,v )*a14*a2 *a7*b2*v + 2*f(v,v )*f(v,v)*a14 *a7 *b2*v)/a2
3x x
df(u,t)=(df(u,x,3)*a2**2 + 3*df(u,x)**2*a14*a2 + 2*df(u,x)*f(v,v)*a14*a7 + f(df(
v,x),df(v,x))*a2*a7 + f(v,df(v,x,2))*a2*a7)/a2$
df(v,t)=(df(u,x,2)*a14*a2*v + 2*df(u,x)*df(v,x)*a14*a2 + df(v,x)*f(v,v)*a14*a7 +
f(v,df(v,x))*a14*a7*v)/a2$
df(u,s)=(df(u,x,5)*a2**4*b2 + 10*df(u,x,3)*df(u,x)*a14*a2**3*b2 + 4*df(u,x,3)*f(
v,v)*a14*a2**2*a7*b2 + 5*df(u,x,2)**2*a14*a2**3*b2 + 10*df(u,x,2)*f(v,df(v,x))*
a14*a2**2*a7*b2 + 10*df(u,x)**3*a14**2*a2**2*b2 + 12*df(u,x)**2*f(v,v)*a14**2*a2
*a7*b2 + 10*df(u,x)*f(df(v,x),df(v,x))*a14*a2**2*a7*b2 + 10*df(u,x)*f(v,df(v,x,2
))*a14*a2**2*a7*b2 + 3*df(u,x)*f(v,v)**2*a14**2*a7**2*b2 + 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 + 3*f(df(v,x),df(v,x))*f(v,
v)*a14*a2*a7**2*b2 + f(v,df(v,x,4))*a2**3*a7*b2 + 3*f(v,df(v,x,2))*f(v,v)*a14*a2
*a7**2*b2 + 3*f(v,df(v,x))**2*a14*a2*a7**2*b2)/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 + 6*df(u,x,
2)*df(u,x)*a14**2*a2**2*b2*v + 3*df(u,x,2)*f(v,v)*a14**2*a2*a7*b2*v + 6*df(u,x)
**2*df(v,x)*a14**2*a2**2*b2 + 6*df(u,x)*df(v,x)*f(v,v)*a14**2*a2*a7*b2 + 6*df(u,
x)*f(v,df(v,x))*a14**2*a2*a7*b2*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 + df(v,x)*f(v,v)**2*a14**2*a7**2*b2
+ 3*f(df(v,x),df(v,x,2))*a14*a2**2*a7*b2*v + f(v,df(v,x,3))*a14*a2**2*a7*b2*v +
2*f(v,df(v,x))*f(v,v)*a14**2*a7**2*b2*v)/a2**4$