Find the sum of the order and degree of the differential equation $y = x(\frac{dy}{dx})^3 + \frac{d^2y}{dx^2}$.

The order and degree of the differential equation $\{1+(\frac{dy}{dx})^2\}^{\frac{3}{2}}=\frac{d^2y}{dx^2}$ are $p$ and $q$ respectively. Then,$p+q=$ . . . . . . .

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is...

For the differential equation $\frac{d^3 y}{d x^3}=0$,$y=a x^2+b x+c$ is

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 number of arbitrary constants in the particular solution of a differential equation of fourth order is . . . . . .