Differential Equations

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Moderate

Solutions of ODEs Using Laplace Transforms 1

DIFFEQ-2SS2WY

Solve the IVP below using the Laplace transform:

$$y' - 2y = 3 t e^{-t}, \quad y(0) = y_0$$

A

$$y(t) = y_0 e^{2t}$$

B

$$y(t) = y_0 e^{t} +\frac{1}{3} e^{t} $$

C

$$y(t) = y_0 e^{2t} +\frac{1}{3} e^{2t} -\frac{1}{3} e^{-t} $$

D

$$y(t) = y_0 e^{2t} +\frac{1}{3} e^{2t} -\frac{1}{3} e^{-t} - t e^{-t}$$