kovacic.spad line 1 [edit on github]
Kovacic provides a modified Kovacic's algorithm for solving explicitly irreducible 2nd order linear ordinary differential equations.
kovacic(a_0,a_1,a_2) returns either "failed" or P(u) such that $e^\int(-a_1/2a_2) e^\int u$ is a solution of a_2 y'' + a_1 y' + a0 y = 0 whenever u is a solution of P u = 0. The equation must be already irreducible over the rational functions.
kovacic(a_0,a_1,a_2,ezfactor) returns either "failed" or P(u) such that $e^\int(-a_1/2a_2) e^\int u$ is a solution of $a_2 y'' + a_1 y' + a0 y = 0$ whenever u is a solution of P u = 0. The equation must be already irreducible over the rational functions. Argument ezfactor is a factorisation in UP, not necessarily into irreducibles.