Differential Equations

Abstract

Maple can solve many ordinary differential equations analytically as explicit functions or in implicit form. Traditional techniques such as the method of Laplace transformations, integrating factors, etc., are available through the differential equation solver dsolve. But modern Lie symmetry methods are implemented as well for partial differential equations in the liesymm package. Approximate methods such as Taylor series and power series methods are also available. And if all fails, one can still use the numerical solver based on the Runge-Kutta method. Moreover, Maple provides all the tools to apply perturbation methods, like the Poincaré-Lindstedt method and the method of multiple scales up to high order. In this chapter, we shall discuss all tools available in Maple for studying differential equations. Many examples come from applied mathematics.