  In this work we present a power series method for solving ordinary and
partial differential equations. To demonstrate our method we solve a system of
ordinary differential equations describing the movement of a random walker on a
one-dimensional lattice, two nonlinear ordinary differential equations, a wave
and diffusion equation (linear partial differential equations), and a nonlinear
partial differential equation (quasilinear). The inclusion of boundary
conditions and the general solutions to other equations of interest are
included in the Supplementary material.
