If $f(x)$ is a polynomial such that $f(x) = [f'(x)]^2$ and $f(2) = 0$, then $f(-2) = \ldots$

The integrating factor of the differential equation $(1 + t^2) + \left(x - e^{\tan^{-1}t}\right)\dfrac{dt}{dx} = 0$ is

The degree of the differential equation obtained from the equation $(y - a)^2 = 4(x - b)$ [where $a$ and b are arbitrary constants] is

The solution of the differential equation $\left(x + 2y^3\right)\dfrac{dy}{dx} - y = 0$ is