1. ## Differential Equations

i Find the value of the constant k such that $\displaystyle y=kx^2e^{-2x}$ is a particular integral of the differential equation:

$\displaystyle \frac{d^2y}{dx^2}+4\frac{dy}{dx}+4y=2e^{-2x}$

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

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

EDIT: Copied this over to the more appropriate forum, you can ignore this.

2. Originally Posted by Lonehwolf
i Find the value of the constant k such that $\displaystyle y=kx^2e^{-2x}$ is a particular integral of the differential equation:

$\displaystyle \frac{d^2y}{dx^2}+4\frac{dy}{dx}+4y=2e^{-2x}$

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

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

EDIT: Copied this over to the more appropriate forum, you can ignore this.
For part (i), subs your particular solution into the ODE and compare LHS to RHS to find k. Where are you stuck on the remaining parts?