of course not soon after I post i find what I am looking for
Euler-Cauchy Linear Homogeneous ODE
Hello. I am looking for some help with 2nd order ODEs that do not have constant coefficients.
I have been looking for pages on the internet to help, either with direct information or examples, but after several hours I couldn't find anything. It may just be that I don't know how to look for exactly what I need.
Here is one:
(x-1)^2*y'' + 4(x-1)*y' + 2y = 0
so I am looking for two solutions (y1, and y2) and then simply the general solution.
So here is what I've done, and I'm not sure if its the right direction or not.
But I found the Wronskian, which turns out to be C/(x-1)^4
using maple, I found out that the 2 solutions I am looking for are:
when I put those two solutions into the matrix, I got the same answer of the Wronksian I found earlier...1/(x-1)^4 where C = 1
so that is all I have been able to conjure up so far. Is there a method to work backwards with the Wronksian to get those 2 desired equations? What do I need to do, from the beginning.
Thanks for any help.