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

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:

The order and degree of a differential equation obtained by eliminating the arbitrary constant $C$ from the family of curves $y^2 = 2C(x + \sqrt{C})$ are respectively:

The order and degree of the differential equation $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$ are

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

The differential equation of all parabolas having their axis of symmetry coinciding with the $x$-axis has its order and degree respectively: