Determine the Laplace transform of the differential equation below with the listed conditions: Consider a system represented by the differential equation $\frac{d ^{2} y ( t )}{d t ^{2}} + 4 \frac{d y ( t )}{d t} + 3 y (t) = 2 r (t)$ where the initial conditions are $y (0) = 1, \frac{d y}{d t} (0) = 0$ , and $r (t) = 1, t ? 0$ .

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Determine the Laplace transform of the differential equation below with the listed conditions: Consider a system represented by the differential equation

\frac{d ^{2} y ( t )}{d t ^{2}} + 4 \frac{d y ( t )}{d t} + 3 y (t) = 2 r (t)

where the initial conditions are

y (0) = 1, \frac{d y}{d t} (0) = 0

, and

r (t) = 1, t ? 0

.

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