y' = (2x)/(y+1). Solve for y.

y' = dy/dx = (2x)/(y+1) Separate x's and y's in this case.

y + 1 dy = 2x dx Now integrate both sides.

(y²)/2 + y = (2x²)/ 2 + C  Don't forget the constant. 

(y²)/2 + y = x² + C