For the differential equation given below,determine its order and degree (if defined):
$\left(\frac{dy}{dx}\right)^{3}-4\left(\frac{dy}{dx}\right)^{2}+7y=\sin x$

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.

Determine the order and degree (if defined) of the differential equation $y''' + 2y'' + y' = 0$.

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

The order and degree of the differential equation of all tangent lines to the parabola $x^2 = 4y$ are respectively:

The order of the differential equation $2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0$ is