Originally Posted by

**s3a** The question asks me to solve x^2 y'' - 5x y' - 7y = x^3 as function of x. In other words, it's asking for y(x). I am given the initial conditions y(1) = 10 and y'(1) = 8.

Someone who wasn't very sure told me to use characteristic equations and the method of undetermined coefficients but is that correct? If so, how do I set it up mechanically? I only know how to use characteristic equations when there are no x variables in the differential equation. I am really, really stuck. I only divided both sides by x^2.

The answer is:

http://www.wolframalpha.com/input/?i=Solve+x^2+y''+-+5xy'+-+7y+%3D+x^3;+y(1)+%3D+10,+y'(1)+%3D+8

If someone could show me how to set up the problem (tedious steps aren't necessary), I would greatly appreciate it!

Thanks in advance!