Solution 2 to problem N1f1b0o24w1

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

Expressions

The solution is given through the following expressions: 

q12=0


         2
     4*p4 *q6
q11=----------
         2
       p3


     3*p4*q6
q10=---------
       p3


        2
    6*p4 *q6
q9=----------
        2
      p3


        2
    4*p4 *q6
q8=----------
        2
      p3


    6*p4*q6
q7=---------
      p3


q5=0


q4=0


q3=0


q2=0


q1=0


p2=0


p1=0


         3
     2*p4 *q6
q13=----------
         3
       p3

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: 
 q6, p3, p4

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. 
 
{p3,

           3                2             2                   2                2
 2*g0020*p4  + 4*g0022*p3*p4  + 3*g0023*p3 *p4 + 6*g0024*p3*p4  + 4*g0025*p3*p4

              2              3
  + 6*g0026*p3 *p4 + g0027*p3 ,

 g0033*p4 + g0034*p3}

Relevance for the application:



The equation: 



f =Df*f *p3 + f  *p4
 t     x       2x


The symmetry: 

                   2                    2                        2
f =(4*Df  *f *p3*p4 *q6 + 6*Df *Df*f *p3 *p4*q6 + 6*Df *f  *p3*p4 *q6
 s      2x  x                 x     x                 x  2x

           3      3            2       2                       2
     + (Df) *f *p3 *q6 + 3*(Df) *f  *p3 *p4*q6 + 4*Df*f  *p3*p4 *q6
              x                   2x                   3x

               3       3
     + 2*f  *p4 *q6)/p3
          4x


And now in machine readable form: 

The system: 

df(f(1),t)=d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,2)*p4$


The symmetry: 

df(f(1),s)=(4*d(1,df(f(1),x,2))*df(f(1),x)*p3*p4**2*q6 + 6*d(1,df(f(1),x))*d(1,f
(1))*df(f(1),x)*p3**2*p4*q6 + 6*d(1,df(f(1),x))*df(f(1),x,2)*p3*p4**2*q6 + d(1,f
(1))**3*df(f(1),x)*p3**3*q6 + 3*d(1,f(1))**2*df(f(1),x,2)*p3**2*p4*q6 + 4*d(1,f(
1))*df(f(1),x,3)*p3*p4**2*q6 + 2*df(f(1),x,4)*p4**3*q6)/p3**3$