The degree of the differential equation $\left( \frac{d^3y}{dx^3} \right)^2 + 4\left( \frac{dy}{dx} \right)^3 = 3\sin \left( \frac{d^2y}{dx^2} \right)$ is:

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.

The order of the differential equation whose solution is ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is:

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

Find the order and degree,if defined,of the following differential equation:
$x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$

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