The degree of the differential equation $\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)^2=x^2 \log \left(\frac{d^2 y}{d x^2}\right)$ is

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{\frac{4}{3}}+x\left(\frac{d y}{d x}\right)^2-y \cos \left(\frac{d y}{d x}\right)=0$ is

The order of the differential equation of all circles of radius $r$,having centre on the $y$-axis and passing through the origin is:

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

The order and degree of the differential equation $e^{\frac{d^2 y}{d x^2}} = x$ are . . . . . . respectively.

The order of the differential equation $\left(\frac{d^3 y}{d x^3}\right)^4+\left(\frac{d^2 y}{d x^2}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$ is . . . . . . .