Solution 1 to problem N1f1b0o35w3

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f1b0o35w3

Expressions

The solution is given through the following expressions: 

     5
    ---*p1*q7
     3
q6=-----------
       p3


     10
    ----*p1*q7
     3
q5=------------
        p3


     10
    ----*p1*q7
     3
q4=------------
        p3


     10    2
    ----*p1 *q7
     9
q3=-------------
          2
        p3


     20    2
    ----*p1 *q7
     9
q2=-------------
          2
        p3


     5
    ---*p1*q7
     3
q1=-----------
       p3


p2=p1

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, p1, 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. 
 
{p1,

 q7,

 p3,

 g0018*p3 + g0019*p1 + g0020*p1,

 p2,

 15*g0003*p3*q7 + 30*g0004*p3*q7 + 30*g0005*p3*q7 + 10*g0006*p1*q7

                                                2             2
  + 20*g0007*p1*q7 + 15*g0008*p3*q7 + 9*g0009*p3  + 9*g0010*p3 ,

           2                                                                 2
 9*g0011*p3  + 15*g0012*p1*p3 + 30*g0013*p1*p3 + 30*g0014*p1*p3 + 10*g0015*p1

               2
  + 20*g0016*p1  + 15*g0017*p1*p3}

Relevance for the application:



The equation: 

f =Df *f*p1 + Df*f *p1 + f  *p3
 t   x            x       3x


The symmetry: 

     5                     10                      20             2
f =(---*Df  *f*p1*p3*q7 + ----*Df  *f *p1*p3*q7 + ----*Df *Df*f*p1 *q7
 s   3    3x               3     2x  x             9     x

        10                      10      2      2       5
     + ----*Df *f  *p1*p3*q7 + ----*(Df) *f *p1 *q7 + ---*Df*f  *p1*p3*q7
        3     x  2x             9          x           3      3x

             2       2
     + f  *p3 *q7)/p3
        5x


And now in machine readable form: 

The equation: 
df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 + d(1,f(1))*df(f(1),x)*p1 + df(f(1),x,3)*p3$


The symmetry: 

df(f(1),s)=(5/3*d(1,df(f(1),x,3))*f(1)*p1*p3*q7 + 10/3*d(1,df(f(1),x,2))*df(f(1)
,x)*p1*p3*q7 + 20/9*d(1,df(f(1),x))*d(1,f(1))*f(1)*p1**2*q7 + 10/3*d(1,df(f(1),x
))*df(f(1),x,2)*p1*p3*q7 + 10/9*d(1,f(1))**2*df(f(1),x)*p1**2*q7 + 5/3*d(1,f(1))
*df(f(1),x,3)*p1*p3*q7 + df(f(1),x,5)*p3**2*q7)/p3**2$