The differential equation whose solution is $Ax^2 + By^2 = 1$,where $A$ and $B$ are arbitrary constants,is of:

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:

If $\alpha$ and $\beta$ are respectively the order and degree of the differential equation $y=e^{\left(\frac{dy}{dx}+\frac{d^2y}{dx^2}\right)}$,then the value of $\alpha+\alpha^\beta+\alpha^{2\beta}+\ldots+\alpha^{2023\beta}$ is:

Find the order and degree of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}+\sin \left(\frac{dy}{dx}\right)\right]^{\frac{3}{4}}=\frac{d^{2}y}{dx^{2}}$.

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

The order and degree of the differential equation $\sqrt{2 + (\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$ are respectively: