Solution 5 to problem N1f1b0o57w3

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

Expressions

The solution is given through the following expressions: 

      5    2
     ---*p7 *q7
      7
q16=------------
          2
        p5


q15=0


     p7*q7
q14=-------
      p5


     2*p7*q7
q13=---------
       p5


     3*p7*q7
q12=---------
       p5


     1
q11=---*q7
     2


q10=q7


    2*p7*q7
q9=---------
      p5


    p7*q7
q8=-------
     p5


    1
q6=---*q7
    2


     1
    ----*p5*q7
     10
q5=------------
        p7


q4=0


q3=0


q2=0


q1=0


p6=p5


p4=p5


     3     2
    ----*p5
     10
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, 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. 
 
{q12,

 p5,

 q7,

 p7,

 p6,

            2                                                                2
 10*g0040*p7  + 10*g0041*p5*p7 + 10*g0042*p5*p7 + 10*g0043*p5*p7 + 3*g0044*p5 ,

 p4,

            2                 2                 2
 10*g0004*p7 *q7 + 20*g0005*p7 *q7 + 30*g0006*p7 *q7 + 5*g0007*p5*p7*q7

                                   2                 2
  + 10*g0008*p5*p7*q7 + 20*g0009*p7 *q7 + 10*g0010*p7 *q7 + 10*g0011*p5*p7*q7

                               2                 2                 2
  + 5*g0012*p5*p7*q7 + g0013*p5 *q7 + 10*g0018*p5 *p7 + 10*g0019*p5 *p7

               2                3
  + 10*g0020*p5 *p7 + 3*g0021*p5 ,

 q9,

            3                 2                  2                  2
 50*g0024*p7  + 70*g0026*p5*p7  + 140*g0027*p5*p7  + 210*g0028*p5*p7

               2                 2                     2                 2
  + 35*g0029*p5 *p7 + 70*g0030*p5 *p7 + 140*g0031*p5*p7  + 70*g0032*p5*p7

               2                 2                3
  + 70*g0033*p5 *p7 + 35*g0034*p5 *p7 + 7*g0035*p5 }

Relevance for the application:



The equation: 



                                     3       2      2                        2
    Df  *f *p5*p7 + Df *f  *p5*p7 + ----*(Df) *f *p5  + Df*f  *p5*p7 + f  *p7
      2x  x           x  2x          10         x           3x          5x
f =----------------------------------------------------------------------------
 t                                      p7


The symmetry: 

                 2                      2                   2
f =(Df  *f *p5*p7 *q7 + 2*Df  *f  *p5*p7 *q7 + Df  *Df*f *p5 *p7*q7
 s    4x  x                 3x  2x               2x     x

                       2       1       2      2                      2
     + 3*Df  *f  *p5*p7 *q7 + ---*(Df ) *f *p5 *p7*q7 + Df *Df*f  *p5 *p7*q7
           2x  3x              2     x    x               x     2x

                      2       1       3      3       1      2       2
     + 2*Df *f  *p5*p7 *q7 + ----*(Df) *f *p5 *q7 + ---*(Df) *f  *p5 *p7*q7
           x  4x              10         x           2         3x

                   2       5        3        2
     + Df*f  *p5*p7 *q7 + ---*f  *p7 *q7)/(p5 *p7)
           5x              7   7x


And now in machine readable form: 

The system: 

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


The symmetry: 

df(f(1),s)=(d(1,df(f(1),x,4))*df(f(1),x)*p5*p7**2*q7 + 2*d(1,df(f(1),x,3))*df(f(
1),x,2)*p5*p7**2*q7 + d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*p5**2*p7*q7 + 3*d(1
,df(f(1),x,2))*df(f(1),x,3)*p5*p7**2*q7 + 1/2*d(1,df(f(1),x))**2*df(f(1),x)*p5**
2*p7*q7 + d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p5**2*p7*q7 + 2*d(1,df(f(1),x))
*df(f(1),x,4)*p5*p7**2*q7 + 1/10*d(1,f(1))**3*df(f(1),x)*p5**3*q7 + 1/2*d(1,f(1)
)**2*df(f(1),x,3)*p5**2*p7*q7 + d(1,f(1))*df(f(1),x,5)*p5*p7**2*q7 + 5/7*df(f(1)
,x,7)*p7**3*q7)/(p5**2*p7)$