I don't understand this at all, and the professor is no help. I have no idea where to start. Please help!
(a) Show that y=ln(1+x) is the solution to the IVP (1+x)y"+y'=0, y(0)=0, y'(0)=1 for x>-1. Then find a power series solution around x0=0, and conclude that this power series is equal to ln(1+x). What is the radius of convergence?
(b) Find a power series solution (around x0=0) to the IVP (1+x)y"+2y'=0, y(0)=1, y'(0)=-1
What is the sum of this power series?