Solution 1 to problem l1o23


Expressions | Parameters | Relevance | Back to problem l1o23

Expressions

The solution is given through the following expressions:

         3       2
      - ---*a4*a8 *b12
         8
b21=-------------------
              3
            a6


         3
      - ---*a4*a8*b12
         4
b20=------------------
             2
           a6


b19=0


         3       3        3       3
      - ---*a1*a8 *b12 + ---*a6*a8 *b12
         4                8
b18=------------------------------------
                      4
                    a6


      3    2
     ---*a8 *b12
      4
b17=-------------
           2
         a6


         9       2        3       2
      - ---*a1*a8 *b12 + ---*a6*a8 *b12
         4                2
b16=------------------------------------
                      3
                    a6


      3
     ---*a8*b12
      2
b15=------------
         a6


      3
     ---*a8*b12
      2
b14=------------
         a6


         3               3
      - ---*a1*a8*b12 + ---*a6*a8*b12
         4               4
b13=----------------------------------
                     2
                   a6


b11=0


b10=0


      3
     ---*a4*a8*b12
      2
 b9=---------------
            2
          a6


     3
    ---*a4*a8*b12
     4
b8=---------------
           2
         a6


     3
    ---*a4*b12
     2
b7=------------
        a6


     3
    ---*a4*b12
     2
b6=------------
        a6


b5=0


     9       2        3       2
    ---*a1*a8 *b12 - ---*a6*a8 *b12
     2                2
b4=---------------------------------
                    3
                  a6


     9               3
    ---*a1*a8*b12 - ---*a6*a8*b12
     2               2
b3=-------------------------------
                   2
                 a6


     9               3
    ---*a1*a8*b12 - ---*a6*a8*b12
     2               2
b2=-------------------------------
                   2
                 a6


     3            1
    ---*a1*b12 - ---*a6*b12
     2            2
b1=-------------------------
              a6


         1
      - ---*a4*a8
         4
a10=--------------
          a6


         1       2    1       2
      - ---*a1*a8  + ---*a6*a8
         2            4
 a9=----------------------------
                  2
                a6


        1           1
     - ---*a1*a8 + ---*a6*a8
        2           2
a7=--------------------------
               a6


a5=0


a3=0


    2*a1*a8
a2=---------
      a6


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:
 b12,a4,a8,a6,a1

Relevance for the application:

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

         u  *a1*a6 + 2*u *a1*a8*u + f(v,v )*a4*a6
          2x            x                x
df(u,t)=------------------------------------------
                            a6

             1                   1       2              3        2
df(v,t)=( - ---*u *a1*a6*a8*v + ---*u *a6 *a8*v + v  *a6  + v *a6 *a8*u
             2   x               2   x             2x        x

             1                       1       2  2      1       2  2      2
          - ---*f(v,v)*a4*a6*a8*v - ---*a1*a8 *u *v + ---*a6*a8 *u *v)/a6
             4                       2                 4

          3           2        1        3        9
df(u,s)=(---*u  *a1*a6 *b12 - ---*u  *a6 *b12 + ---*u  *a1*a6*a8*b12*u
          2   3x               2   3x            2   2x

             3        2             9    2                 3    2   2
          - ---*u  *a6 *a8*b12*u + ---*u  *a1*a6*a8*b12 - ---*u  *a6 *a8*b12
             2   2x                 2   x                  2   x

             3                            9          2      2
          + ---*u *f(v,v)*a4*a6*a8*b12 + ---*u *a1*a8 *b12*u
             4   x                        2   x

             3          2      2    3                2
          - ---*u *a6*a8 *b12*u  + ---*f(v ,v )*a4*a6 *b12
             2   x                  2     x  x

             3                2        3                            3
          + ---*f(v,v  )*a4*a6 *b12 + ---*f(v,v )*a4*a6*a8*b12*u)/a6
             2       2x                2       x

             3           2             3        3
df(v,s)=( - ---*u  *a1*a6 *a8*b12*v + ---*u  *a6 *a8*b12*v
             4   2x                    4   2x

             3          3           9             2
          + ---*u *v *a6 *a8*b12 - ---*u *a1*a6*a8 *b12*u*v
             2   x  x               4   x

             3       2   2                 4        3        3
          + ---*u *a6 *a8 *b12*u*v + v  *a6 *b12 + ---*v  *a6 *a8*b12*u
             2   x                    3x            2   2x

             3       2   2      2    3               2
          + ---*v *a6 *a8 *b12*u  - ---*f(v,v )*a4*a6 *a8*b12*v
             4   x                   4       x

             3                 2            3       3      3
          - ---*f(v,v)*a4*a6*a8 *b12*u*v - ---*a1*a8 *b12*u *v
             8                              4

             3       3      3      4
          + ---*a6*a8 *b12*u *v)/a6
             8