Let δ be the unit impulse (zero away from its point and total integral 1). Solve $2y^{\prime\prime}+y^\prime+2y=\delta(x-5)$, y(0) = y′(0) = 0. Which y(10) is correct?
Laplace transformation gives $Y(s)=e^{-5s}/(2s^2+s+2)$. Complete the square: denominator is $2[(s+1/4)^2+15/16]$. The impulse response is $h(t)=2e^{-t/4}\sin(\sqrt{15}t/4)/\sqrt{15}$. Shift by five, then evaluate t = 10, giving h(5), **B**.
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