The order of the differential equation $y \left( \frac{dy}{dx} \right) = \frac{x}{\frac{dy}{dx} + \left( \frac{dy}{dx} \right)^3}$ is

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

If $m$ and $n$ are the order and degree of the differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1$,then:

The degree of the differential equation $(1 + \frac{dy}{dx})^2 = (\frac{d^3y}{dx^3})^{1/3}$ is . . . . . . .

The order and degree of the differential equation $y = x \frac{dp}{dx} + \sqrt{a^{2} p^{2} + b^{2}}$,where $p = \frac{dy}{dx}$ (here $a$ and $b$ are arbitrary constants) respectively are:

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$ are respectively: