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This page titled 17.4: Series Solutions of Differential Equations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Gilbert Strang & Edwin “Jed” Herman (OpenStax) via source content that was edited to the style and standards of the LibreTexts platform.

This page titled 4.2: Power Series Method is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Russell Herman via source content that was edited to the style and standards of the LibreTexts platform.

Assuming you know how to find a power series solution for a linear differential equation around the point #x_0#, you just have to expand the source term into a Taylor series around #x_0# and proceed as usual.

This may add considerable effort to the solution and if the power series solution can be identified as an elementary function, it''s generally easier to just solve the homogeneous equation and use either the method of undetermined coefficients or the method of variation of parameters.

where #c_0# is any constant.

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