Solution 4 to problem l1o35

Expressions | Parameters | Relevance | Back to problem l1o35

Expressions

The solution is given through the following expressions:


b75=0

b74=(4*a12*a14*b2)/a2**2

b73=(2*a12*a14*b2)/a2**2

b72=0

b71=0

b70=0

b69=0

b68=0

b67=0

b66=0

b65=0

b64=0

b63=0

b62=0

b61=0

b60=0

b59=0

b58=0

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=(6*a12*a14*b2)/a2**2

b32=(8*a12*b2)/a2

b31=(4*a12*b2)/a2

b30=(4*a12*b2)/a2

b29=0

b28=0

b27=0

b26=0

b25=0

b24=0

b23=0

b22=0

b21=0

b20=0

b19=0

b18=0

b17=0

b16=0

b15=0

b14=0

b13=0

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=0

a20=0

a19=0

a18=0

a17=0

a16=0

a15=2*a14

a13=0

a11=0

a10=0

a9=0

a8=0

a7=0

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,a14,a12,a2

Relevance for the application:

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$

                     2             2
df(u,t)=u  *a2 + 3*u  *a14 + f(v,v) *a12
         3x         x

df(v,t)=u  *a14*v + 2*u *v *a14
         2x            x  x

               2                                 2                  3    2
df(u,s)=(u  *a2 *b2 + 10*u  *u *a14*a2*b2 + 5*u   *a14*a2*b2 + 10*u  *a14 *b2
          5x              3x  x                2x                  x

                       2
          + 6*u *f(v,v) *a12*a14*b2 + 4*f(v ,v )*f(v,v)*a12*a2*b2
               x                           x  x

                                                   2              2
          + 4*f(v,v  )*f(v,v)*a12*a2*b2 + 8*f(v,v ) *a12*a2*b2)/a2
                   2x                            x

                                                            2
df(v,s)=(u  *a14*a2*b2*v + 2*u  *v *a14*a2*b2 + 6*u  *u *a14 *b2*v
          4x                  3x  x                2x  x

                2       2                 2
          + 6*u  *v *a14 *b2 + 2*v *f(v,v) *a12*a14*b2
               x   x              x

                                             2
          + 4*f(v,v )*f(v,v)*a12*a14*b2*v)/a2
                   x

df(u,t)=df(u,x,3)*a2 + 3*df(u,x)**2*a14 + f(v,v)**2*a12$

df(v,t)=df(u,x,2)*a14*v + 2*df(u,x)*df(v,x)*a14$

df(u,s)=(df(u,x,5)*a2**2*b2 + 10*df(u,x,3)*df(u,x)*a14*a2*b2 + 5*df(u,x,2)**2*
a14*a2*b2 + 10*df(u,x)**3*a14**2*b2 + 6*df(u,x)*f(v,v)**2*a12*a14*b2 + 4*f(df(v,
x),df(v,x))*f(v,v)*a12*a2*b2 + 4*f(v,df(v,x,2))*f(v,v)*a12*a2*b2 + 8*f(v,df(v,x)
)**2*a12*a2*b2)/a2**2$

df(v,s)=(df(u,x,4)*a14*a2*b2*v + 2*df(u,x,3)*df(v,x)*a14*a2*b2 + 6*df(u,x,2)*df(
u,x)*a14**2*b2*v + 6*df(u,x)**2*df(v,x)*a14**2*b2 + 2*df(v,x)*f(v,v)**2*a12*a14*
b2 + 4*f(v,df(v,x))*f(v,v)*a12*a14*b2*v)/a2**2$