Calculus differential question???

Question

Using implicit differentiation determine whether the given relation is an implicit solution to the given differental equation.

y - ln(y) = x^2 + 1 , dy/dx = 2xy/y-1 ..... I don't think it is I need verification

Answer 1

y´-y´/y=2x so y´( 1-1/y) =2x and y´=dy/dx= 2xy/(y-1) which is your differential equation