Multivariable Calculus

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Moderate

Determine General Solution of y'' - 2y' - 8y = 2t^2

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Determine the general solution for the differential equation:

$$y'' - 2y' - 8y = 2t^2$$

A

$y(t) = - \frac{t^2}{4} + \frac{t}{8} - \frac{3}{32}$

B

$y(t) = c_1 e^{-2t} + c_2 e^{4t} - \frac{t^2}{4} + \frac{t}{8} - \frac{3}{32}$

C

$y(t) = c_1 e^{-2t} + c_2 e^{4t} + 2t^2$

D

$y(t) = c_1 e^{2t} + c_2 e^{-4t} + 2t^2$

E

None of the Above