Determine the order and degree (if defined) of the differential equation $y^{\prime} + y = e^{x}$.

The degree of the differential equation $x = 1 + \left(\frac{dy}{dx}\right) + \frac{1}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{1}{3!} \left(\frac{dy}{dx}\right)^3 + \dots$ is:

The order and degree of the differential equation $\sqrt{1 + \frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}$ are ...

The degree of the differential equation $\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^3 + 6y = 0$ is

The degree and order of the differential equation $y = x(\frac{dy}{dx})^2 + \frac{dy}{dx}$ are respectively:

The order of the differential equation whose solution is $y = a\cos x + b\sin x + c{e^{ - x}}$ is