Determine the order and degree (if defined) of the differential equation $y^{\prime} + y = e^{x}$.

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.

The degree of the differential equation $1+\left(\frac{dy}{dx}\right)^2+\left(\frac{d^2y}{dx^2}\right)^2=\sqrt[3]{\frac{d^2y}{dx^2}+1}$ 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 of the differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}+2 x^2\left(\frac{d^2 y}{d x^2}\right)^{\frac{5}{3}}+7 \frac{d y}{d x}+y=0$ is:

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