In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
It is given that y = Ax
Now, differentiating both sides w.r.t. x, we get,
⇒ y’ = A
Now, Substituting the values of y’ in the given differential equations, we get,
xy’ = x.A = Ax = y = RHS.
Therefore, the given function is the solution of the corresponding differential equation.