Solution 30 to problem l112o23

Expressions | Parameters | Relevance | Back to problem l112o23

Expressions

The solution is given through the following expressions:


      1      2       3       1      3   3
     ----*a12 *a14*a5 *b4 - ----*a14 *a5 *b24
      48                     64
b42=------------------------------------------
                          6
                       a12


         1     2       2       3      3   2
      - ---*a12 *a14*a5 *b4 + ----*a14 *a5 *b24
         8                     32
b41=--------------------------------------------
                           5
                        a12


         1            2       3     2   2
      - ---*a12*a14*a5 *b2 + ---*a14 *a5 *b24
         4                    8
b40=------------------------------------------
                          4
                       a12


      3      2   2
     ----*a14 *a5 *b24
      16
b39=-------------------
              4
           a12


      1     2              3      3
     ---*a12 *a14*a5*b4 - ----*a14 *a5*b24
      4                    16
b38=---------------------------------------
                        4
                     a12


      1                   3     2
     ---*a12*a14*a5*b2 - ---*a14 *a5*b24
      2                   4
b37=-------------------------------------
                       3
                    a12


         3     2
      - ---*a14 *a5*b24
         4
b36=--------------------
               3
            a12


      1                   3     2
     ---*a12*a14*a5*b2 - ---*a14 *a5*b24
      4                   8
b35=-------------------------------------
                       3
                    a12


      1               1
     ---*a14*a5*b1 - ---*a14*a5*b24
      2               2
b34=--------------------------------
                     2
                  a12


      1               1
     ---*a14*a5*b1 - ---*a14*a5*b24
      2               2
b33=--------------------------------
                     2
                  a12


         3
      - ---*a14*a5*b24
         2
b32=-------------------
              2
           a12


         3
      - ---*a14*a5*b24
         4
b31=-------------------
              2
           a12


         1     2           1     3
      - ---*a12 *a14*b4 + ---*a14 *b24
         6                 8
b30=-----------------------------------
                      3
                   a12


      3     2
     ---*a14 *b24
      4
b29=--------------
            2
         a12


         1                3     2
      - ---*a12*a14*b2 + ---*a14 *b24
         2                4
b28=----------------------------------
                      2
                   a12


      3
     ---*a14*b24
      2
b27=-------------
         a12


      3
     ---*a14*b24
      2
b26=-------------
         a12


         1            1
      - ---*a14*b1 + ---*a14*b24
         2            2
b25=-----------------------------
                 a12


      1      2       4       1      3   4
     ----*a12 *a14*a5 *b4 - ----*a14 *a5 *b24
      48                     64
b23=------------------------------------------
                          7
                       a12


         1     2       3       3      3   3
      - ---*a12 *a14*a5 *b4 + ----*a14 *a5 *b24
         8                     32
b22=--------------------------------------------
                           6
                        a12


         1     2   3       1            3       9      2   3
      - ---*a12 *a5 *b4 - ---*a12*a14*a5 *b2 + ----*a14 *a5 *b24
         4                 4                    16
b21=-------------------------------------------------------------
                                   5
                                a12


      1     2       2       3      3   2
     ---*a12 *a14*a5 *b4 - ----*a14 *a5 *b24
      4                     16
b20=-----------------------------------------
                         5
                      a12


        2   2       1            2       3     2   2
     a12 *a5 *b4 + ---*a12*a14*a5 *b2 - ---*a14 *a5 *b24
                    2                    2
b19=-----------------------------------------------------
                               4
                            a12


      1     2   2       1            2       3     2   2
     ---*a12 *a5 *b4 + ---*a12*a14*a5 *b2 - ---*a14 *a5 *b24
      4                 4                    8
b18=---------------------------------------------------------
                                 4
                              a12


           2       3        2
     a12*a5 *b2 - ---*a14*a5 *b24
                   2
b17=------------------------------
                    3
                 a12


      1        2       1        2       5        2
     ---*a12*a5 *b2 + ---*a14*a5 *b1 - ---*a14*a5 *b24
      2                2                4
b16=---------------------------------------------------
                              3
                           a12


      1        2       1        2       1        2
     ---*a12*a5 *b2 + ---*a14*a5 *b1 - ---*a14*a5 *b24
      2                2                2
b15=---------------------------------------------------
                              3
                           a12


         1     2              1     3
      - ---*a12 *a14*a5*b4 + ---*a14 *a5*b24
         6                    8
b14=-----------------------------------------
                         4
                      a12


           2          3     2
      - a12 *a5*b4 + ---*a14 *a5*b24
                      4
b13=---------------------------------
                     3
                  a12


           2          1                   3     2
      - a12 *a5*b4 - ---*a12*a14*a5*b2 + ---*a14 *a5*b24
                      2                   4
b12=-----------------------------------------------------
                               3
                            a12


                     3
      - a12*a5*b2 + ---*a14*a5*b24
                     2
b11=-------------------------------
                    2
                 a12


      - a5*b2
b10=----------
       a12


                      3
     - 2*a12*a5*b2 + ---*a14*a5*b24
                      2
b9=---------------------------------
                    2
                 a12


        1               1               1
     - ---*a12*a5*b2 - ---*a14*a5*b1 + ---*a14*a5*b24
        2               2               2
b8=---------------------------------------------------
                             2
                          a12


     - a5*b1 + a5*b24
b7=-------------------
           a12


     - 3*a5*b1
b6=------------
       a12


b5=0


b3=b2


      1      2   2
     ----*a14 *a5
      16
a19=---------------
            3
         a12


         1     2
      - ---*a14 *a5
         4
a18=----------------
             2
          a12


         1
      - ---*a14*a5
         2
a17=---------------
          a12


         1
      - ---*a14*a5
         2
a16=---------------
          a12


      1     2
     ---*a14
      4
a15=----------
       a12


     1
a13=---*a14
     2


      1      2   3
     ----*a14 *a5
      16
a11=---------------
            4
         a12


         1     2   2
      - ---*a14 *a5
         4
a10=-----------------
             3
          a12


             2
     - a14*a5
a9=------------
          2
       a12


     1     2
    ---*a14 *a5
     4
a8=-------------
          2
       a12


    a14*a5
a7=--------
     a12


     1
    ---*a14*a5
     2
a6=------------
       a12


a4=0


a3=0


a2=0


a1=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:

 b4,b2,b24,b1,a5,a14,a12

Relevance for the application:

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

          1               3                      4
df(u,t)=(---*u *f(v,v)*a12 *a14*a5 + f(v,v  )*a12 *a5
          2   x                           2x

                              2       2              3
          - f(v,v )*f(v,v)*a12 *a14*a5  + f(v,v )*a12 *a14*a5*u
                 x                             x

             1         3    2   3    1        2        2   2
          + ----*f(v,v) *a14 *a5  - ---*f(v,v) *a12*a14 *a5 *u
             16                      4

             1            2    2     2     4
          + ---*f(v,v)*a12 *a14 *a5*u )/a12
             4

          1        3                4    1               2
df(v,t)=(---*u *a12 *a14*v + v  *a12  - ---*v *f(v,v)*a12 *a14*a5
          2   x               2x         2   x

                  3          1             2             1         2    2   2
          + v *a12 *a14*u - ---*f(v,v )*a12 *a14*a5*v + ----*f(v,v) *a14 *a5 *v
             x               2       x                   16

             1                2           1     2    2  2       3
          - ---*f(v,v)*a12*a14 *a5*u*v + ---*a12 *a14 *u *v)/a12
             4                            4

                7       1                6          1                5
df(u,s)=(u  *a12 *b1 - ---*u  *f(v,v)*a12 *a5*b2 - ---*u  *f(v,v)*a12 *a14*a5*b1
          3x            2   2x                      2   2x

             1                5                     7          2    7
          + ---*u  *f(v,v)*a12 *a14*a5*b24 + u  *a12 *b2*u + u  *a12 *b2
             2   2x                           2x              x

                            6          3                5
          - 2*u *f(v,v )*a12 *a5*b2 + ---*u *f(v,v )*a12 *a14*a5*b24
               x      x                2   x      x

             1           2    5   2       1           2    4       2
          + ---*u *f(v,v) *a12 *a5 *b4 + ---*u *f(v,v) *a12 *a14*a5 *b2
             4   x                        4   x

             3           2    3    2   2                    6
          - ---*u *f(v,v) *a12 *a14 *a5 *b24 - u *f(v,v)*a12 *a5*b4*u
             8   x                              x

             1               5                3               4    2
          - ---*u *f(v,v)*a12 *a14*a5*b2*u + ---*u *f(v,v)*a12 *a14 *a5*b24*u
             2   x                            4   x

                  7     2                  6
          + u *a12 *b4*u  - 3*f(v ,v  )*a12 *a5*b1
             x                   x  2x

             1                     5   2
          + ---*f(v ,v )*f(v,v)*a12 *a5 *b2
             2     x  x

             1                     4       2
          + ---*f(v ,v )*f(v,v)*a12 *a14*a5 *b1
             2     x  x

             1                     4       2                   6
          - ---*f(v ,v )*f(v,v)*a12 *a14*a5 *b24 - f(v ,v )*a12 *a5*b2*u
             2     x  x                               x  x

                        6                     6
          - f(v,v  )*a12 *a5*b1 + f(v,v  )*a12 *a5*b24
                 3x                    3x

             1                     5   2
          + ---*f(v,v  )*f(v,v)*a12 *a5 *b2
             2       2x

             1                     4       2
          + ---*f(v,v  )*f(v,v)*a12 *a14*a5 *b1
             2       2x

             5                     4       2                   6
          - ---*f(v,v  )*f(v,v)*a12 *a14*a5 *b24 - f(v,v  )*a12 *a5*b2*u
             4       2x                                 2x

             3              5                       2    5   2
          + ---*f(v,v  )*a12 *a14*a5*b24*u + f(v,v ) *a12 *a5 *b2
             2       2x                           x

             3         2    4       2        1                2    4   3
          - ---*f(v,v ) *a12 *a14*a5 *b24 - ---*f(v,v )*f(v,v) *a12 *a5 *b4
             2       x                       4       x

             1                2    3       3
          - ---*f(v,v )*f(v,v) *a12 *a14*a5 *b2
             4       x

             9                 2    2    2   3
          + ----*f(v,v )*f(v,v) *a12 *a14 *a5 *b24
             16       x

                              5   2         1                    4       2
          + f(v,v )*f(v,v)*a12 *a5 *b4*u + ---*f(v,v )*f(v,v)*a12 *a14*a5 *b2*u
                 x                          2       x

             3                    3    2   2                    6        2
          - ---*f(v,v )*f(v,v)*a12 *a14 *a5 *b24*u - f(v,v )*a12 *a5*b4*u
             2       x                                    x

             3             4    2         2    1         4    2       4
          + ---*f(v,v )*a12 *a14 *a5*b24*u  + ----*f(v,v) *a12 *a14*a5 *b4
             4       x                         48

             1         4    3   4        1        3    3       3
          - ----*f(v,v) *a14 *a5 *b24 - ---*f(v,v) *a12 *a14*a5 *b4*u
             64                          8

             3         3        3   3          1        2    4       2     2
          + ----*f(v,v) *a12*a14 *a5 *b24*u + ---*f(v,v) *a12 *a14*a5 *b4*u
             32                                4

             3         2    2    3   2      2    1            5            3
          - ----*f(v,v) *a12 *a14 *a5 *b24*u  - ---*f(v,v)*a12 *a14*a5*b4*u
             16                                  6

             1            3    3         3     7
          + ---*f(v,v)*a12 *a14 *a5*b24*u )/a12
             8

             1         5             1         5
df(v,s)=( - ---*u  *a12 *a14*b1*v + ---*u  *a12 *a14*b24*v
             2   2x                  2   2x

             3           5            1               4
          + ---*u *v *a12 *a14*b24 + ---*u *f(v,v)*a12 *a14*a5*b2*v
             2   x  x                 4   x

             3               3    2             1        5
          - ---*u *f(v,v)*a12 *a14 *a5*b24*v - ---*u *a12 *a14*b2*u*v
             8   x                              2   x

             3        4    2                  6
          + ---*u *a12 *a14 *b24*u*v + v  *a12 *b24
             4   x                      3x

             3                4               3         5
          - ---*v  *f(v,v)*a12 *a14*a5*b24 + ---*v  *a12 *a14*b24*u
             4   2x                           2   2x

             3                4               3            2    2    2   2
          - ---*v *f(v,v )*a12 *a14*a5*b24 + ----*v *f(v,v) *a12 *a14 *a5 *b24
             2   x      x                     16   x

             3               3    2             3        4    2      2
          - ---*v *f(v,v)*a12 *a14 *a5*b24*u + ---*v *a12 *a14 *b24*u
             4   x                              4   x

             1              4                1              4
          + ---*f(v ,v )*a12 *a14*a5*b1*v - ---*f(v ,v )*a12 *a14*a5*b24*v
             2     x  x                      2     x  x

             1              4                1              4
          + ---*f(v,v  )*a12 *a14*a5*b1*v - ---*f(v,v  )*a12 *a14*a5*b24*v
             2       2x                      2       2x

             1                    3       2
          - ---*f(v,v )*f(v,v)*a12 *a14*a5 *b2*v
             4       x

             3                    2    2   2
          + ---*f(v,v )*f(v,v)*a12 *a14 *a5 *b24*v
             8       x

             1             4                  3             3    2
          + ---*f(v,v )*a12 *a14*a5*b2*u*v - ---*f(v,v )*a12 *a14 *a5*b24*u*v
             2       x                        4       x

             1         3    2       3         1         3    3   3
          + ----*f(v,v) *a12 *a14*a5 *b4*v - ----*f(v,v) *a14 *a5 *b24*v
             48                               64

             1        2    3       2           3         2        3   2
          - ---*f(v,v) *a12 *a14*a5 *b4*u*v + ----*f(v,v) *a12*a14 *a5 *b24*u*v
             8                                 32

             1            4            2      3             2    3         2
          + ---*f(v,v)*a12 *a14*a5*b4*u *v - ----*f(v,v)*a12 *a14 *a5*b24*u *v
             4                                16

             1     5         3      1     3    3      3       6
          - ---*a12 *a14*b4*u *v + ---*a12 *a14 *b24*u *v)/a12
             6                      8