Solution 4 to problem N1f1b0o24w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o24w1

Expressions

The solution is given through the following expressions:


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q5=0


q3=0


q2=0


q1=0


p4=0


p2=0


    3*p1*q6
p3=---------
      q4

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:

 q4, q6, 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.

 
{g0027*p3 + 3*g0029*p1,p1,g0034*p3 + g0036*p1}

Relevance for the application:

The equation:


    Df *f*p1*q4 + 3*Df*f *p1*q6
      x                 x
f =-----------------------------
 t              q4

The symmetry:

           2            3
f =Df *(Df) *f*q4 + (Df) *f *q6
 s   x                     x

And now in machine readable form:

The system:

df(f(1),t)=(d(1,df(f(1),x))*f(1)*p1*q4 + 3*d(1,f(1))*df(f(1),x)*p1*q6)/q4$

The symmetry:

df(f(1),s)=d(1,df(f(1),x))*d(1,f(1))**2*f(1)*q4 + d(1,f(1))**3*df(f(1),x)*q6$