Solution 8 to problem N1f1b0o57w3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o57w3

Expressions

The solution is given through the following expressions:


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q3=0


q2=0


q1=0


p7=0


p6=0


p5=0


p4=0


p1=0


    3*p2*q5
p3=---------
     2*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, q5, p2

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.

 
{2*g0035*p3 + 3*g0036*p2,p2,g0044*p3 + g0045*p2}

Relevance for the application:

The equation:


                      3      2
    Df *Df*f*p2*q4 + ---*(Df) *f *p2*q5
      x               2         x
f =-------------------------------------
 t                  q4

The symmetry:

           2            3
f =Df *(Df) *f*q4 + (Df) *f *q5
 s   x                     x

And now in machine readable form:

The system:

df(f(1),t)=(d(1,df(f(1),x))*d(1,f(1))*f(1)*p2*q4 + 3/2*d(1,f(1))**2*df(f(1),x)*
p2*q5)/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)*q5$