I'm trying to (re-)teach myself differential equations, and I've run into a snag. Say I have a differential equation which includes the solution on the RHS. How can I solve this, I think I can put it into standard form, but then I get stuck. Say I have
where P is the function I'm trying to obtain. I would think I could put this in standard form like so
with an integrating factor of
So I'd get
I know that the solution is the following, but I'm not sure of how to get there.
Any help would be appreciated.