The sum of the order and degree of the differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{2}}=\left(1+\frac{d y}{d x}\right)^{\frac{4}{3}}$ is

The differential equation $\frac{d^3y}{dx^3}-5y \frac{dy}{dx}+xy=0$ represents :-

Determine the order and degree (if defined) of the differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$.

The number of arbitrary constants in the particular solution of a differential equation of third order is:

The order and degree of the differential equation $e^{\frac{d^2 y}{d x^2}} = x$ are . . . . . . respectively.

The order and degree of the differential equation $(\frac{d^3y}{dx^3}+y\frac{dy}{dx})^{\frac{7}{5}} =x^3\frac{d^2y}{dx^2}$ are $m$ and $n$ respectively,then $(m + n)$ is equal to-