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-

The order and degree of the differential equation $\sqrt[3]{\frac{d^2 y}{d x^2}}=\sqrt{\frac{d^3 y}{d x^3}}$ are . . . . . . and . . . . . . .

The order of the differential equation $\frac{d^2 y}{d x^2}=\sqrt{1-\left(\frac{d y}{d x}\right)^2}$ is

The order of the differential equation whose general solution is given by $y = C_1 e^{2x + C_2} + C_3 e^x + C_4 \sin(x + C_5)$ 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:

Statement $1$: The degrees of the differential equations $\frac{dy}{dx} + y^2 = x$ and $\frac{d^2y}{dx^2} + y = \sin x$ are equal.
Statement $2$: The degree of a differential equation,when it is a polynomial equation in derivatives,is the highest positive integral power of the highest order derivative involved in the differential equation; otherwise,the degree is not defined.