Determine the order and degree (if defined) of the differential equation $y^{\prime \prime} + 2y^{\prime} + \sin(y) = 0$.

Which of the following equations is non-linear?

The order and degree of the differential equation $x\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 + y^2 = 0$ are respectively:

Determine the order and degree (if defined) of the differential equation $\left(\frac{ds}{dt}\right)^{4} + 3s \frac{d^{2}s}{dt^{2}} = 0$.

If $m$ and $n$ are the order and degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^5 + 4\frac{\left( \frac{d^2y}{dx^2} \right)^3}{\left( \frac{d^3y}{dx^3} \right)} + \frac{d^3y}{dx^3} = x^2 - 1$,then

If $y=a^3 e^{b^2 x+c}$ is the general solution of a differential equation,where $a$ and $c$ are arbitrary constants and $b$ is a fixed constant,then the order of the differential equation is