Could someone help me solve the following:
y'' +(1/3x)y' - (1/3x)y = 0
I go through the steps I would normally to solve the DE, but when attempting to find the roots I end up with a function of x which I'm not exactly sure what to do with. It appears that there must be different solutions for different ranges of x. How would I go about solving this?
You are correct, we just need to switch our variables around to obtain the required equation for the Frobenius method: Frobenius method - Wikipedia, the free encyclopedia
Where,
Then continue with the Frobenius method. There is an excellent example on that wikipedia page (first example) that will walk you through all the steps (so I won't repeat them here out of lazyness).