The order and degree of the differential equation $\sqrt[4]{\left(\frac{d^3 y}{d x^3}\right)^5} = \sqrt[3]{\left(\frac{d^2 y}{d x^2}\right)^4}$ are . . . . . . and . . . . . . respectively.

For the differential equation given below,determine its order and degree (if defined):
$\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x$

Determine the order and degree (if defined) of the differential equation $\frac{d^4y}{dx^4} + \sin(y''') = 0$.

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.

Which of the following equations is non-linear?

The degree and order of the differential equation $y = x(\frac{dy}{dx})^2 + \frac{dy}{dx}$ are respectively: