A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where $0 \leq \mathrm{t}<3$)

The order of the differential equation, whose general solution is given by

$$y=\left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 e^{x+c 5}$$

where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constant, is

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0

The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y+1}{x+y-1}$ is