iFind the value of the constant k such that $\displaystyle y=kx^2e^{-2x}$ is a particular integral of the differential equation: $\displaystyle \frac{d^2y}{dx^2}+4\frac{dy}{dx}+4y=2e^{-2x}$

iiFind the solution of this differential equation for which y=1 and $\displaystyle \frac{dy}{dx}=0$ when x=0.

iiiUse the differential equation to determine the value of $\displaystyle \frac{d^2y}{dx^2}$ when x=0. Hence prove that 0<=1 for x>0