t^2*y^'' -t(t+2)y^' + (t+2)y=0 , t>0; ysub1(t) = t
Reduction of order:
A second solution is assumed to be of the form:
ysub2(t) = v(t)*ysub1(t)
The Attempt at a Solution
So, the algebra in the first part of the process seemed to be correct, as it cancelled out all the "v" terms and left only derivatives of v. The problem seems to happen somewhere around when I turn it into a first order linear equation and attempt to multiply through by an integrating factor. As far as I, and a CAS are concerned, that integral at the end is not possible to take. This leaves the assumption that I completely goofed up my integrating factor. Where could I have gone wrong?