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Differential Equations

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The Laplace Transform of a Differential Operator

DIFFEQ-VG34IL

Consider the equation $y''+2y'+3y=4e^t$ with initial values $y(0)=-1, y'(0)=2$.

The Laplace Transform of the left hand side $\mathcal{L}(y''+2y'+3y)$ is:

A

$s^2Y(s)+2sY(s)+3Y(s)$

B

$s^2Y(s)+2sY(s)+3Y(s)+s$

C

$s^2Y(s)+2sY(s)+3Y(s)-2s+3$

D

None of the above