Verifying a Solution for a Basic Differential Equation

[TG3]

Homework Statement
Show that y = x-(x^-1) is a solution for the differential equations:
xy' +y = 2x

The attempt at a solution
Frankly, I haven't a clue how to start.

If it weren't for the x in the xy' term this would be easy, since I could just integrate; unfortunately, I don't know how to separate the x's from the y's, and this is really a problem, because this is the first problem from the homework set. I re-read the textbook, but don't get it. Any suggestions for techniques to separate the variables?

 

[Nabeshin]

The problem isn't asking you to solve the differential equation, merely to verify that the solution given is in fact a solution. So, substitute it in for y and y' and see if the equation holds true.