Degree of the differential equation $e^{\frac{dy}{dx}} + (\frac{dy}{dx})^3 = x$ is

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

The differential equation $\frac{d^2y}{dx^2} + x\frac{dy}{dx} + \sin y + x^2 = 0$ is of the following type:

If $y=a^3 e^{b^2 x+c}$ is the general solution of a differential equation,where $a$ and $c$ are arbitrary constants and $b$ is a fixed constant,then the order of the differential equation 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.

The degree of the differential equation $x = 1 + \left(\frac{dy}{dx}\right) + \frac{1}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{1}{3!} \left(\frac{dy}{dx}\right)^3 + \dots$ is: