kovacicODE
**********

Introduction to kovacicODE
==========================

Definitions for kovacicODE
==========================

 -- 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)]