Solve y′=1x+yy' = \frac{1}{x+y}y′=x+y1 is not standard, but consider y′=1y+1y' = \frac{1}{y} + 1y′=y1+1. What is the transformation for y2=uy^2 = uy2=u?
u′=2+2uu' = 2 + 2\sqrt{u}u′=2+2u
u′=1+2uu' = 1 + 2uu′=1+2u
u′=2(1+u)u' = 2(1 + \sqrt{u})u′=2(1+u)
u′=2+uu' = 2 + uu′=2+u