Solution 1 to problem N1t8s14f5

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s14f5

Expressions

The solution is given through the following expressions:


q8=0


q7=0


q6=0


q5=0


q4=0


q2=0


p3=0


    2*p1*q3
q1=---------
      p2

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:

 q3, p2, p1

Inequalities

In the following not identically vanishing expressions are shown. Any auxiliary variables g00?? are used to express that at least one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3 means that either p4 or p3 or both are non-vanishing.

 
{g0023*p2 + g0024*p1,g0019*p2 + 2*g0021*p1}

Relevance for the application:

The equation:


f =Df *f*p1 + Df*f *p2
 t   x            x

The symmetry:

                           2
    2*Df *Df*f*p1*q3 + (Df) *f *p2*q3
        x                     x
f =-----------------------------------
 s                 p2

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 + d(1,f(1))*df(f(1),x)*p2$

The symmetry:

df(f(1),s)=(2*d(1,df(f(1),x))*d(1,f(1))*f(1)*p1*q3 + d(1,f(1))**2*df(f(1),x)*p2*
q3)/p2$