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Differential Equations

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IVP: Stair Forcing

DIFFEQ-NGHKLG

Consider the equation $3y''-2y'+y=g(t)$ with initial conditions $y(0)=1, y'(0)=2$. Suppose that $g$ is $1$ on $[1,3]$, $2$ on $[3,6]$ and zero everywhere else.

Find the Laplace Transform of $y$:

A

$\cfrac{6s+1}{3s^2-2s+1}+\cfrac{e^{-s}+e^{-3s}-2e^{-6s}}{s(3s^2-2s+1)}$

B

$\cfrac{3s+4}{3s^2-2s+1}+\cfrac{2e^{-6s}-e^{-s}-e^{-3s}}{s(3s^2-2s+1)}$

C

$\cfrac{6s+1}{3s^2-2s+1}+\cfrac{2e^{-6s}-e^{-s}-e^{-3s}}{s(3s^2-2s+1)}$

D

$\cfrac{3s+4}{3s^2-2s+1}+\cfrac{e^{-s}+e^{-3s}-2e^{-6s}}{s(3s^2-2s+1)}$