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I'm trying to solve 2 questions for my assignment on homogeneous ODEs

I can solve ODE's with variation of parameters and with the method of undetermined coefficients, but these 2 methods seem useless when the coefficients are not constant :

(x^2)y" - 2xy' -54y = 0

and

(x^2)y" - 3xy' + 4y = 0

I'm not asking anyone to solve it for me, but just to tell me what method I have to use, and I'll find on my book or on the net.

P.S : I know that you can use power series method, but I think there is another one since we are learning the power series method right now, with a brand new homework just on power series!

Thanks guys

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# Homework Help: Homogeneous ODE with variable coefficient

**Physics Forums | Science Articles, Homework Help, Discussion**