The integrating factor of the differential equation $x\dfrac{dy}{dx} + 2y = x^2 \log x$ is

A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius $r$ with time '$t$' is $\ldots$ (where $k$ is a positive constant)

The order and degree of the differential equation $\sqrt{1 + \dfrac{1}{\left(\dfrac{dy}{dx}\right)^2}} = \left(\dfrac{d^2y}{dx^2}\right)^{\frac{3}{2}}$ are $\ldots$

The equation of the curve whose slope is $\dfrac{y-1}{x^2+x}$ and which passes through the point $(1, 0)$ is