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

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

y = x² + 2x + C : y′ – 2x – 2 = 0

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

y = cos x + C : y′ + sin x = 0

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

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)

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

y = x sin x : xy′ = y + x (x ≠ 0 and x > y or x < – y)

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

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

y – cos y = x : (y sin y + cos y + x)y′ = y

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

x + y = tan^–1y : y²y′ + y² + 1 = 0

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

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

The number of arbitrary constants in the particular solution of a differential equation of third order are: