Determine the order and degree (if defined) of the differential equation $y''' + 2y'' + y' = 0$.

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

The degree of the given differential equation $\left( \frac{d^2y}{dx^2} \right)^3 = \left( 1 + \frac{dy}{dx} \right)^{1/2}$ is:

The order and degree of the differential equation $3 - (\frac{d^3y}{dx^3})^{7/3} = (\frac{dy}{dx})^5$ are respectively

$p$ and $q$ are positive integers and $n < r < m$. If the order and degree of the differential equation $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^{p/q} = 5 \frac{d^r y}{d x^r}$ are respectively $4$ and $3$,then:

The order and degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^3 + \left( \frac{dy}{dx} \right)^4 - xy = 0$ are respectively: