Solution 2 to problem N1f1b0o35w3


Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o35w3

Expressions

The solution is given through the following expressions:

    2*p3*q3
q6=---------
      p2


    2*p3*q3
q5=---------
      p2


    2*p3*q3
q4=---------
      p2


q2=0


q1=0


p1=0


        2
    6*p3 *q3
q7=----------
         2
     5*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, p3

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                                                                2
{6*g0011*p3  + 10*g0012*p2*p3 + 10*g0013*p2*p3 + 10*g0014*p2*p3 + 5*g0015*p2 ,

 p2,

 g0018*p3 + g0019*p2}


Relevance for the application:



The equation: 
f =Df*f *p2 + f  *p3
 t     x       3x
The symmetry:
                                                  2      2
f =(2*Df  *f *p2*p3*q3 + 2*Df *f  *p2*p3*q3 + (Df) *f *p2 *q3
 s      2x  x                x  2x                   x

                            6        2       2
     + 2*Df*f  *p2*p3*q3 + ---*f  *p3 *q3)/p2
             3x             5   5x
And now in machine readable form:

The equation:

df(f(1),t)=d(1,f(1))*df(f(1),x)*p2 + df(f(1),x,3)*p3$
The symmetry:
df(f(1),s)=(2*d(1,df(f(1),x,2))*df(f(1),x)*p2*p3*q3 + 2*d(1,df(f(1),x))*df(f(1),
x,2)*p2*p3*q3 + d(1,f(1))**2*df(f(1),x)*p2**2*q3 + 2*d(1,f(1))*df(f(1),x,3)*p2*
p3*q3 + 6/5*df(f(1),x,5)*p3**2*q3)/p2**2$