solve-

Question

dy/dx = 2xy + (y^2/x^2)

Answer 1

Looks like a Riccati equation. Standard methods, such as those at

http://www.sosmath.com/diffeq/first/riccati/riccati.html

will lead to the solution

y = xe^(x^2) / (cx + e^(x^2) - πix erf(ix))

where erf(x) is the error function.

Answer 2

Use wolframalpha dot com - it will solve yr equation and show all steps.