The solution of the differential equation ydydx=x ex2+y2 is

Given equation can be written as  ye−y2dy=xex2dx               ( variables separable method)      ⇒∫2xex2⋅dx=−∫(−2y)e−y2⋅dy⇒∫etdt=−∫eu⋅du where t=x2 and u=−y2⇒ex2=−e−y2+c⇒ex2+e−y2=c