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I know how to find the solution to a 2nd order homogeneous with constant coefficients but how do you solve one with a non constant

ie

x^2y''+2xy' ....... etc = 0

Is there a general solution formula for these types of problems?

My book seems to jump from 2nd order homogeneous with constant coefficients straight to

2nd order non homogeneous with undetermined coefficients.

any help greatly appreciated.

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# 2nd order homogeneous

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