Solution 6 to problem N1f1b0o35w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o35w1

Expressions

The solution is given through the following expressions:


q20=0


q19=0


      5
     ---*p5*q21
      3
q18=------------
         p7


q17=0


q16=0


q15=0


      5
     ---*p5*q21
      3
q14=------------
         p7


q13=0


      5
     ---*p5*q21
      3
q12=------------
         p7


q11=0


      10    2
     ----*p5 *q21
      9
q10=--------------
           2
         p7


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p6=0


p4=0


p3=0


p2=0


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:

 q21, p5, p7

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.

 
{q21,

 p7,

 g0050*p7 + g0052*p5,

           2                                                                 2
 9*g0029*p7  + 15*g0032*p5*p7 + 15*g0036*p5*p7 + 15*g0038*p5*p7 + 10*g0040*p5 ,

 p5,

 15*g0005*p7*q21 + 15*g0009*p7*q21 + 15*g0011*p7*q21 + 10*g0013*p5*q21

              2
  + 9*g0024*p7 }

Relevance for the application:

The equation:


f =Df *f *p5 + f  *p7
 t   x  x       3x

The symmetry:

     5                       5                        10       2      2
f =(---*Df  *f *p5*p7*q21 + ---*Df  *f  *p5*p7*q21 + ----*(Df ) *f *p5 *q21
 s   3    3x  x              3    2x  2x              9      x    x

        5                            2        2
     + ---*Df *f  *p5*p7*q21 + f  *p7 *q21)/p7
        3    x  3x              5x

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*df(f(1),x)*p5 + df(f(1),x,3)*p7$

The symmetry:

df(f(1),s)=(5/3*d(1,df(f(1),x,3))*df(f(1),x)*p5*p7*q21 + 5/3*d(1,df(f(1),x,2))*
df(f(1),x,2)*p5*p7*q21 + 10/9*d(1,df(f(1),x))**2*df(f(1),x)*p5**2*q21 + 5/3*d(1,
df(f(1),x))*df(f(1),x,3)*p5*p7*q21 + df(f(1),x,5)*p7**2*q21)/p7**2$