Verify that given function (explicit or implicit), `y = e^x + 1` is a solution of differential equation `y- y' = 1`.

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = e^x + 1 : y'' - y' = 0

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = Ax : xy' = y(x ne 0)

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = sqrt(1+x^2) : y = (xy)/(1+x^2)

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = cosx +C : y +sinx = 0

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = x sinx : xy' = y + x sqrt(x^2 - y^2)

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = x^2 + 2x + C : y' - 2x - 2 = 0

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y = sqrt(a^2 - x^2) x in (-a, a): x + y (dy)/dx = 0 (y ne 0)

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: y - cosy = x : (y siny + cosy + x) y' = y

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: xy = logy +C : y' = (y^2/(1-xy)) (xy ne 1)

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation: x + y = tan^(-1)y : y^2y' + y^2 + 1 = 0