Solve y′=2xy−xy' = 2xy - xy′=2xy−x by inspection or integrating factor.
y=12+Cex2y = \frac{1}{2} + Ce^{x^2}y=21+Cex2
y=12+Ce−x2y = \frac{1}{2} + Ce^{-x^2}y=21+Ce−x2
y=x2+Cy = x^2 + Cy=x2+C
y=Cex2y = Ce^{x^2}y=Cex2