List of top Differential Equations Questions on Dirac Delta Function and Impulse Response

Let \(\delta(t)\) be the unit impulse function defined by \(\delta(x-x_0)=0\) when \(x\ne x_0\) and \(\displaystyle\int_{-\infty}^{\infty}\delta(x-x_0)\,dx=1\).
Consider the following initial value problem \[ 2\frac{d^2y}{dx^2}+\frac{dy}{dx}+2y=\delta(x-5) \] with \(y(0)=0\) and \(\dfrac{dy}{dx}(0)=0\). Which one of the following is TRUE?