Solution 1 to problem N1t2s6f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t2s6f1

Expressions

The solution is given through the following expressions:


p1=0

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:

 q7, q6, q5, q4, q3, q2, q1, 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.

 
{g0012*q7 + g0013*q6 + g0014*q5 + g0015*q4 + g0016*q3 + g0017*q2 + g0018*q1,

 g0005*q6 + g0006*q5 + g0007*q4 + g0008*q3 + g0009*q2 + g0010*q1,

 p2}

Relevance for the application:

The equation:


f =f *p2
 t  x

The symmetry:

                                             3            2
f =Df  *f*q1 + Df *Df*f*q2 + Df *f *q5 + (Df) *f*q3 + (Df) *f *q4 + Df*f  *q6
 s   2x          x             x  x                          x          2x

 + f  *q7
    3x

And now in machine readable form:

The system:

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

The symmetry:

df(f(1),s)=d(1,df(f(1),x,2))*f(1)*q1 + d(1,df(f(1),x))*d(1,f(1))*f(1)*q2 + d(1,
df(f(1),x))*df(f(1),x)*q5 + d(1,f(1))**3*f(1)*q3 + d(1,f(1))**2*df(f(1),x)*q4 + 
d(1,f(1))*df(f(1),x,2)*q6 + df(f(1),x,3)*q7$