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Before using power series to solve Equation 1, we illustrate the method on the simpler equation in Example 1. EXAMPLE 1 Use power series to solve the equation . Power series solutions. 1.1. An example. So far we can effectively solve linear equations (homogeneous and non-homongeneous) with constant coefficients, 8.1 Introduction and Review of Power Series. In Section 3.3 we saw that solving a homogeneous linear differential equation with constant coefficients can be Many functions can be written in terms of a power series. ∞. ∑ k=0 ak(x − x0)k. If we assume that a solution of a differential equation is written as aSeries Solutions of Differential Equations. 1125. 15.5. S E C T I O N Use a power series to solve the differential equation. Solution Assume that.