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

y = e^x + 1 : y′′ – y′ = 0

It is given that y = e^x + 1

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

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

⇒ y” = e^x

Now, Substituting the values of y’ and y” in the given differential equations, we get,

y” – y’ = e^x - e^x = RHS.

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