If $y(x)$ is the solution of the differential equation $(x+2) \frac{\mathrm{d} y}{\mathrm{~d} x}=x^2+4 x-9, x \neq-2$ and $y(0)=0$, then $y(-4)$ is equal to

The bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 8 hours, then the number of bacteria in 24 hours will be

The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$ is

The particular solution of the differential equation, $x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=x^2+2 y^2$ when $y(1)=0$ is