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

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

The order of the differential equation $y = c_{1} e^{c_{2}+x} + c_{3} e^{c_{4}+x}$ is

The order of the differential equation,whose general solution is given by $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$,where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constants,is

The degree and order of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^3\right]^{\frac{7}{3}}=7\left(\frac{d^2y}{dx^2}\right)$ respectively are

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: