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Differential Equations

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Laplace Transform by Equation

DIFFEQ-JVSJEX

Consider the IVP(initial value problem):

$$y''+4y=\delta(t-\pi)$$
$$y(0)=1$$
$$y'(0)=0$$

...where $\delta$ is the Dirac delta function or the impulse function. The Laplace transform of $y$ is:

A

$\cfrac{s+1}{s^2+4}$

B

$\cfrac{e^{-\pi s}}{s^2+4}$

C

$\cfrac{s}{s^2+4}$

D

$\cfrac{s+e^{-\pi s}}{s^2+4}$