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

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

$p$ 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 product of the degree and order of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^2-\left(\frac{d y}{d x}\right)^3=y^3$ is

The order and degree of the differential equation $\left[1+\frac{1}{(\frac{dy}{dx})^{2}}\right]^{\frac{5}{3}}=5 \frac{d^{2}y}{dx^{2}}$ are respectively:

Which of the following equations is non-linear?