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7.4 Series Solutions of Differential Equations

Let us solve the differential equation y'' = y by Power Series Method. Let y = ∞ ∑ n=0cnxn, where cn is to be determined. By taking derivatives term by term, y' = ∞ ∑ n=1ncnxn−1

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6.2: The Power Series Method The power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with

Assume the differential equation has a solution of the form y(x) = ∞ ∑ n = 0anxn. Differentiate the power series term by term to get y′ (x) = ∞ ∑ n = 1nanxn − 1 and y″ (x) = ∞ ∑ n

This article covers power series solutions of linear differential equations, recurrence relations, linear algebra, theorems, corollaries, applications, and the Cauchy-Euler equation.