The number of arbitrary constants in a particular solution of a differential equation is . . . . . . .

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

Which of the following equations is non-linear?

If $l$ and $m$ are respectively the order and the degree of the differential equation $f(x) y^{\prime \prime}+g(x) y^{\prime}=\frac{4 y}{x}$ whose general solution is $y=a x^2+b \log x$, then $f(m)+g(m)=$

The degree of the differential equation $x = 1 + \left(\frac{dy}{dx}\right) + \frac{1}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{1}{3!} \left(\frac{dy}{dx}\right)^3 + \dots$ is:

The order and degree of the differential equation $\frac{d^3 y}{d x^3} = \left[1 + \left(\frac{d y}{d x}\right)^2\right]^{5/2}$ are respectively: