Solution 1 to problem N1t7s12f4


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t7s12f4

Expressions

The solution is given through the following expressions:

q3=0


    2*p1*q2
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:
 q2, 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.
 
{g0006*p2 + 2*g0007*p1,g0008*p2 + g0009*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*q2 + (Df) *f *p2*q2
        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*q2 + d(1,f(1))**2*df(f(1),x)*p2*
q2)/p2$