In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

xy = log y + C :

It is given that xy = log y + C

Now, differentiating both sides w.r.t. x, we get,

⇒ y + xy’ =

⇒ y² + xyy’ = y’

⇒ (xy – 1)y’ = -y²

⇒ y’ =

Thus, LHS = RHS

Therefore, the given function is the solution of the corresponding differential equation.