In this Chapter, the power series method for generating linearly independent
solutions to ordinary differential equations is considered. The method is applied to the Bessel,
Hypergeometric, Legendre and Airy equations. Some special topics for transforming nonlinear
equations to linear ones by the change of variables are considered, including corresponding
Maple examples for obtaining symbolic and numeric solutions to ordinary differential
equations using power series and other special functions.
Keywords: Airy equations, Bessel, Hypergeometric, Linearly independent solutions, Legendre equations, Numeric solutions, Maple software, Power series method, Special functions, Symbolic solutions.
