The power series technique can also be used to solve non homogeneous differential equations of the form y′′+ p(x)y′+q(x)y =r(x), providedthat p, q,andr are analytic at the point about which we are expanding.  determine terms up to x6 in the power series representation of the general solution to the given differential equation centered at x = 0. Identify those terms in your solution that correspond to the complementary function and those that correspond to a particular solution to the differential equation. Q. y′′+xy′−4y =6ex.

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: 2y" + 9ху ' - 36у %3D 0

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A: I have given the answer in the next step. Hope you understand that

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A: The power series solution is given as follows :

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A: Differential equation is              (x2-2x)y" + 2y = 0

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