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

The order of the differential equation whose solution is $y = a\cos x + b\sin x + c{e^{ - x}}$ is

The degree of the differential equation $\frac{d^2y}{dx^2} - \sqrt{\frac{dy}{dx} - 3} = x$ is

Find the order and degree,if defined,of the following differential equation:
$x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$

For the differential equation $\frac{d^3y}{dx^3} + \cos(\frac{d^2y}{dx^2}) = 0$, which of the following is true?

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: