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?