Solution 4 to problem N1t6s10f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t6s10f1

Expressions

The solution is given through the following expressions: 

q20=0


q19=0


q18=0


      5
     ---*p2*q21
      3
q17=------------
         p7


q16=0


     5*p2*q21
q15=----------
        p7


q14=0


q13=0


q12=0


     5*p2*q21
q11=----------
        p7


      10
     ----*p2*q21
      3
q10=-------------
         p7


q9=0


     10    2
    ----*p2 *q21
     9
q8=--------------
          2
        p7


q7=0


q6=0


     20    2
    ----*p2 *q21
     9
q5=--------------
          2
        p7


     10
    ----*p2*q21
     3
q4=-------------
        p7


q3=0


     5
    ---*p2*q21
     3
q2=------------
        p7


q1=0


p6=0


p5=0


p4=p2


p3=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, p2, 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. 
 
{g0052*p7 + g0055*p2 + g0057*p2,

 p4,

 p2,

 q21,

 p7,

           2
 9*g0031*p7  + 15*g0035*p2*p7 + 45*g0037*p2*p7 + 45*g0041*p2*p7 + 30*g0042*p2*p7

               2              2
  + 10*g0044*p2  + 20*g0047*p2  + 30*g0048*p2*p7 + 15*g0050*p2*p7,

 q10,

 15*g0008*p7*q21 + 45*g0010*p7*q21 + 45*g0014*p7*q21 + 30*g0015*p7*q21

  + 10*g0017*p2*q21 + 20*g0020*p2*q21 + 30*g0021*p7*q21 + 15*g0023*p7*q21

              2             2
  + 9*g0027*p7  + 9*g0029*p7 }

Relevance for the application:



The equation: 



                     2
f =Df *Df*f*p2 + (Df) *f *p2 + f  *p7
 t   x                  x       3x


The symmetry: 

     5                         10
f =(---*Df  *Df*f*p2*p7*q21 + ----*Df  *Df *f*p2*p7*q21 + 5*Df  *Df*f *p2*p7*q21
 s   3    3x                   3     2x   x                   2x     x

        10       2                 20          3     2
     + ----*(Df ) *f *p2*p7*q21 + ----*Df *(Df) *f*p2 *q21
        3      x    x              9     x

                                 10      4      2        5      2
     + 5*Df *Df*f  *p2*p7*q21 + ----*(Df) *f *p2 *q21 + ---*(Df) *f  *p2*p7*q21
           x     2x              9          x            3         3x

             2        2
     + f  *p7 *q21)/p7
        5x


And now in machine readable form: 

The system: 

df(f(1),t)=d(1,df(f(1),x))*d(1,f(1))*f(1)*p2 + d(1,f(1))**2*df(f(1),x)*p2 + df(f
(1),x,3)*p7$


The symmetry: 

df(f(1),s)=(5/3*d(1,df(f(1),x,3))*d(1,f(1))*f(1)*p2*p7*q21 + 10/3*d(1,df(f(1),x,
2))*d(1,df(f(1),x))*f(1)*p2*p7*q21 + 5*d(1,df(f(1),x,2))*d(1,f(1))*df(f(1),x)*p2
*p7*q21 + 10/3*d(1,df(f(1),x))**2*df(f(1),x)*p2*p7*q21 + 20/9*d(1,df(f(1),x))*d(
1,f(1))**3*f(1)*p2**2*q21 + 5*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*p2*p7*q21 +
 10/9*d(1,f(1))**4*df(f(1),x)*p2**2*q21 + 5/3*d(1,f(1))**2*df(f(1),x,3)*p2*p7*
q21 + df(f(1),x,5)*p7**2*q21)/p7**2$