Solution 6 to problem N1f1b0o57w3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o57w3

Expressions

The solution is given through the following expressions: 

      25    2
     ----*p7 *q7
      28
q16=-------------
           2
         p4


q15=0


      5
     ---*p7*q7
      4
q14=-----------
        p4


      5
     ---*p7*q7
      4
q13=-----------
        p4


      5
     ---*p7*q7
      2
q12=-----------
        p4


     1
q11=---*q7
     2


     1
q10=---*q7
     2


     5
    ---*p7*q7
     4
q9=-----------
       p4


     5
    ---*p7*q7
     4
q8=-----------
       p4


    1
q6=---*q7
    4


     1
    ----*p4*q7
     15
q5=------------
        p7


q4=0


q3=0


q2=0


q1=0


p6=p4


p5=0


     1    2
    ---*p4
     5
p3=---------
      p7


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: 
 q7, p4, 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. 
 
{q12,

 q7,

 p4,

 p7,

 p6,

           2                                           2
 5*g0040*p7  + 5*g0041*p4*p7 + 5*g0043*p4*p7 + g0044*p4 ,

            2                 2                  2
 75*g0004*p7 *q7 + 75*g0005*p7 *q7 + 150*g0006*p7 *q7 + 30*g0007*p4*p7*q7

                                   2                 2
  + 30*g0008*p4*p7*q7 + 75*g0009*p7 *q7 + 75*g0010*p7 *q7 + 60*g0011*p4*p7*q7

                                  2                 2                 2
  + 15*g0012*p4*p7*q7 + 4*g0013*p4 *q7 + 60*g0018*p4 *p7 + 60*g0020*p4 *p7

               3
  + 12*g0021*p4 ,

 q9,

             3                  2                  2                   2
 375*g0024*p7  + 525*g0026*p4*p7  + 525*g0027*p4*p7  + 1050*g0028*p4*p7

                2                  2                     2                  2
  + 210*g0029*p4 *p7 + 210*g0030*p4 *p7 + 525*g0031*p4*p7  + 525*g0032*p4*p7

                2                  2                 3
  + 420*g0033*p4 *p7 + 105*g0034*p4 *p7 + 28*g0035*p4 }

Relevance for the application:



The equation: 



                     1      2      2                        2
    Df  *f *p4*p7 + ---*(Df) *f *p4  + Df*f  *p4*p7 + f  *p7
      2x  x          5         x           3x          5x
f =-----------------------------------------------------------
 t                             p7


The symmetry: 

     5               2       5                2                   2
f =(---*Df  *f *p4*p7 *q7 + ---*Df  *f  *p4*p7 *q7 + Df  *Df*f *p4 *p7*q7
 s   4    4x  x              4    3x  2x               2x     x

        5                2       1       2      2
     + ---*Df  *f  *p4*p7 *q7 + ---*(Df ) *f *p4 *p7*q7
        2    2x  3x              4     x    x

        1               2          5               2       1       3      3
     + ---*Df *Df*f  *p4 *p7*q7 + ---*Df *f  *p4*p7 *q7 + ----*(Df) *f *p4 *q7
        2    x     2x              4    x  4x              15         x

        1      2       2          5              2       25        3        2
     + ---*(Df) *f  *p4 *p7*q7 + ---*Df*f  *p4*p7 *q7 + ----*f  *p7 *q7)/(p4 *p7
        2         3x              4      5x              28   7x

   )


And now in machine readable form: 

The system: 

df(f(1),t)=(d(1,df(f(1),x,2))*df(f(1),x)*p4*p7 + 1/5*d(1,f(1))**2*df(f(1),x)*p4
**2 + d(1,f(1))*df(f(1),x,3)*p4*p7 + df(f(1),x,5)*p7**2)/p7$


The symmetry: 

df(f(1),s)=(5/4*d(1,df(f(1),x,4))*df(f(1),x)*p4*p7**2*q7 + 5/4*d(1,df(f(1),x,3))
*df(f(1),x,2)*p4*p7**2*q7 + d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*p4**2*p7*q7 +
 5/2*d(1,df(f(1),x,2))*df(f(1),x,3)*p4*p7**2*q7 + 1/4*d(1,df(f(1),x))**2*df(f(1)
,x)*p4**2*p7*q7 + 1/2*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p4**2*p7*q7 + 5/4*d
(1,df(f(1),x))*df(f(1),x,4)*p4*p7**2*q7 + 1/15*d(1,f(1))**3*df(f(1),x)*p4**3*q7 
+ 1/2*d(1,f(1))**2*df(f(1),x,3)*p4**2*p7*q7 + 5/4*d(1,f(1))*df(f(1),x,5)*p4*p7**
2*q7 + 25/28*df(f(1),x,7)*p7**3*q7)/(p4**2*p7)$