The purpose of this study is to investigate the solutions of initial and boundary value problems of ordinary differential equations by employing Lie symmetry generators. In this investigation, it shown that invariant curves, which obtained by symmetry generators, also be utilized to find solutions to initial and boundary value problems. A method, involving invariant curves, presented to find solutions to initial and boundary value problems. Solutions to many linear and nonlinear initial and boundary value problems discussed by applying the proposed method.