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Determine the general solution for the differential equation:

$$y'' + 2y' + y = \frac{e^{-t}}{t}$$

A

$y(t) = c_1 e^{-t} + c_2te^{-t} + \frac{e^{-t}}{t}$

B

$y(t) = c_1 e^{-t} + c_2te^{-t} + e^{-t}\ln t$

C

$y(t) = c_1 e^{-t} + c_2te^{-t} + \frac{e^{-t}\ln t}{t}$

D

$y(t) = c_1 e^{-t} + c_2te^{-t} + te^{-t}\ln t$

E

None of the Above

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