Solution 12 to problem l1o35

Expressions | Parameters | Relevance | Back to problem l1o35

Expressions

The solution is given through the following expressions:


b75=0

b74=0

b73=0

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=(5/9*a15*a7*b37)/a13**2

b57=0

b56=0

b55=0

b54=0

b53=0

b52=0

b51=0

b50=0

b49=0

b48=0

b47=0

b46=(5/6*a15**2*b37)/a13**2

b45=0

b44=0

b43=0

b42=0

b41=(5/3*a15*b37)/a13

b40=(5/3*a15*b37)/a13

b39=(5/3*a15*b37)/a13

b38=0

b36=0

b35=0

b34=0

b33=0

b32=0

b31=0

b30=0

b29=0

b28=0

b27=0

b26=0

b25=0

b24=0

b23=0

b22=0

b21=0

b20=0

b19=0

b18=(5/3*a15*a7*b37)/a13**2

b17=0

b16=0

b15=0

b14=(10/3*a7*b37)/a13

b13=(5/3*a7*b37)/a13

b12=0

b11=0

b10=0

b9=0

b8=(5/18*a15**2*b37)/a13**2

b7=0

b6=0

b5=(5/6*a15*b37)/a13

b4=(5/3*a15*b37)/a13

b3=0

b2=b37

a22=0

a21=0

a20=0

a19=0

a18=0

a17=0

a16=0

a14=0

a12=0

a11=0

a10=0

a9=0

a8=0

a6=0

a5=0

a4=1/2*a15

a3=0

a2=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:

 b37,a7,a15,a13

Relevance for the application:

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

                   1    2
df(u,t)=u  *a13 + ---*u  *a15 + f(v ,v )*a7
         3x        2   x           x  x

df(v,t)=u *v *a15 + v  *a13
         x  x        3x

                2        5                        5     2
df(u,s)=(u  *a13 *b37 + ---*u  *u *a13*a15*b37 + ---*u   *a13*a15*b37
          5x             3   3x  x                6   2x

             5     3    2        5
          + ----*u  *a15 *b37 + ---*u *f(v ,v )*a15*a7*b37
             18   x              3   x    x  x

             5                           10                           2
          + ---*f(v  ,v  )*a13*a7*b37 + ----*f(v ,v  )*a13*a7*b37)/a13
             3     2x  2x                3      x  3x

          5                        5                         5    2       2
df(v,s)=(---*u  *v *a13*a15*b37 + ---*u  *v  *a13*a15*b37 + ---*u  *v *a15 *b37
          3   3x  x                3   2x  2x                6   x   x

             5                              2        5
          + ---*u *v  *a13*a15*b37 + v  *a13 *b37 + ---*v *f(v ,v )*a15*a7*b37)/
             3   x  3x                5x             9   x    x  x

   2
a13

df(u,t)=df(u,x,3)*a13 + 1/2*df(u,x)**2*a15 + f(df(v,x),df(v,x))*a7$

df(v,t)=df(u,x)*df(v,x)*a15 + df(v,x,3)*a13$

df(u,s)=(df(u,x,5)*a13**2*b37 + 5/3*df(u,x,3)*df(u,x)*a13*a15*b37 + 5/6*df(u,x,2
)**2*a13*a15*b37 + 5/18*df(u,x)**3*a15**2*b37 + 5/3*df(u,x)*f(df(v,x),df(v,x))*
a15*a7*b37 + 5/3*f(df(v,x,2),df(v,x,2))*a13*a7*b37 + 10/3*f(df(v,x),df(v,x,3))*
a13*a7*b37)/a13**2$

df(v,s)=(5/3*df(u,x,3)*df(v,x)*a13*a15*b37 + 5/3*df(u,x,2)*df(v,x,2)*a13*a15*b37
 + 5/6*df(u,x)**2*df(v,x)*a15**2*b37 + 5/3*df(u,x)*df(v,x,3)*a13*a15*b37 + df(v,
x,5)*a13**2*b37 + 5/9*df(v,x)*f(df(v,x),df(v,x))*a15*a7*b37)/a13**2$