(kovacicODE.info)Definitions for kovacicODE

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1.2 Definitions for kovacicODE
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 -- Function: kovacicODE (<expr>, <y>, <x>)

     'kovacicODE' is an implementation of the Kovacic algorithm for
     finding the solution of second order linear ordinary differential
     equations (ODEs) with Liouvillian solutions.  If the ODE has a
     Liouvillian solution, 'kovacicODE' finds and returns the solution.
     If the ODE does not have a Liouvillian solution, 'kovacicODE'
     returns 'false'.

     'load("kovacicODE")' loads this function.

     Example:

     Example 1 from "On Liouvillian Solutions of Linear Differential
     Equations" by F. Unger (1992), Applicable Algebra in Engineering,
     Communication and Computing, volume 2, issue 3, pp 171-193.
     'DEBUGFLAG' controls debugging output in 'kovacicODE'; we'll set it
     to 0 to suppress debugging output in this example.

          (%i1) load (kovacicODE) $
          (%i2) eq : 'diff(y,x,2) - 'diff(y,x,1)/x+x^2*y/(x^4+2*x^2+1) = 0;
                                  dy
                             2    --        2
                            d y   dx       x  y
          (%o2)             --- - -- + ------------- = 0
                              2   x     4      2
                            dx         x  + 2 x  + 1
          (%i3) DEBUGFLAG : 0 $
          (%i4) kovacicODE (eq, y, x);
                               2           2                  2
          (%o4) [y = %k2 sqrt(x  + 1) log(x  + 1) + %k1 sqrt(x  + 1)]