# Kovacic(F, UP)¶

Kovacic provides a modified Kovacic's algorithm for solving explicitely 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.