Solution 2 to problem N1f1b0o37w3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o37w3

Expressions

The solution is given through the following expressions: 

q15=0


          2
     18*p3 *q5
q14=-----------
           2
       5*p2


          2
     36*p3 *q5
q13=-----------
           2
       5*p2


          2
     54*p3 *q5
q12=-----------
           2
       5*p2


     3*p3*q5
q11=---------
       p2


     6*p3*q5
q10=---------
       p2


         2
    36*p3 *q5
q9=-----------
          2
      5*p2


         2
    18*p3 *q5
q8=-----------
          2
      5*p2


    6*p3*q5
q7=---------
      p2


    3*p3*q5
q6=---------
      p2


q4=0


q3=0


q2=0


q1=0


p1=0


          3
     54*p3 *q5
q16=-----------
           3
      35*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: 
 q5, 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. 
 
            3                  2                  2                  2
{54*g0022*p3  + 126*g0024*p2*p3  + 252*g0025*p2*p3  + 378*g0026*p2*p3

                2                  2                     2                  2
  + 105*g0027*p2 *p3 + 210*g0028*p2 *p3 + 252*g0029*p2*p3  + 126*g0030*p2*p3

                2                  2                 3
  + 210*g0031*p2 *p3 + 105*g0032*p2 *p3 + 35*g0033*p2 ,

 p2,

 g0038*p3 + g0039*p2}

Relevance for the application:



The equation: 



f =Df*f *p2 + f  *p3
 t     x       3x


The symmetry: 

     18               2       36                2                     2
f =(----*Df  *f *p2*p3 *q5 + ----*Df  *f  *p2*p3 *q5 + 6*Df  *Df*f *p2 *p3*q5
 s   5     4x  x              5     3x  2x                 2x     x

        54                2             2      2                        2
     + ----*Df  *f  *p2*p3 *q5 + 3*(Df ) *f *p2 *p3*q5 + 6*Df *Df*f  *p2 *p3*q5
        5     2x  3x                  x    x                 x     2x

        36               2          3      3            2       2
     + ----*Df *f  *p2*p3 *q5 + (Df) *f *p2 *q5 + 3*(Df) *f  *p2 *p3*q5
        5     x  4x                    x                   3x

        18              2       54        3       3
     + ----*Df*f  *p2*p3 *q5 + ----*f  *p3 *q5)/p2
        5       5x              35   7x


And now in machine readable form: 

The system: 

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)=(18/5*d(1,df(f(1),x,4))*df(f(1),x)*p2*p3**2*q5 + 36/5*d(1,df(f(1),x,3
))*df(f(1),x,2)*p2*p3**2*q5 + 6*d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*p2**2*p3*
q5 + 54/5*d(1,df(f(1),x,2))*df(f(1),x,3)*p2*p3**2*q5 + 3*d(1,df(f(1),x))**2*df(f
(1),x)*p2**2*p3*q5 + 6*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p2**2*p3*q5 + 36/5
*d(1,df(f(1),x))*df(f(1),x,4)*p2*p3**2*q5 + d(1,f(1))**3*df(f(1),x)*p2**3*q5 + 3
*d(1,f(1))**2*df(f(1),x,3)*p2**2*p3*q5 + 18/5*d(1,f(1))*df(f(1),x,5)*p2*p3**2*q5
 + 54/35*df(f(1),x,7)*p3**3*q5)/p2**3$