..Solve the following differential equation:
Well, an appropriate substitution would be , so that
After dividing both sides by x, and substituting the above, we get
This is separable, but how do you integrate the RHS? Or could we just say, like what we do in linear DE's, that
, and then integrate both sides? Mr F says: No. The integration would have to be wrt x, but the right hand side is a function of u. You have to seperate and integrate. The integral wrt u is certainly non-elementary. I'd re-check the question for a typo.
Although unusual (and gives what looks like a simpler integral to solve), I don't think can be integrated using elementary functions.
Can anyone see a way out?