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Differential Equations

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Moderate

An Initial Value Problem

DIFFEQ-31EELR

The solution to the initial value problem:

$$\begin{equation} y' - y = 4 e^{2t}\\\ y(0) = 0 \end{equation}$$

...is:

A

$y(t) = 4(1 - e^{t})$

B

$y(t) = 4(e^{2t}-e^{t})$

C

$y(t) = 4(e^{2t}-e^{-t})$

D

$y(t) = 4(e^{-2t}-e^{t})$