Question: Develop series solutions for Hermite's differential equation dy dy 2x- + 2ay = 0 dx? d.x (a) Find the indicial equation and the recurrence

Develop series solutions for Hermite's differential equation dy dy 2x- + 2ay

Develop series solutions for Hermite's differential equation dy dy 2x- + 2ay = 0 dx? d.x (a) Find the indicial equation and the recurrence relations for two roots of the indicial equation. (b) Show that both series are convergent for all x. (c) Find solutions for a =0 and a = 1.

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