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Differential Equations

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Solution to a Forced Differential Equation

DIFFEQ-IEXWUS

The solution to:

$$\begin{equation} y'' + 25y = \cos 3t + 4 \sin 2t, y(0) = 0, y'(0) = 1 \end{equation}$$

...is:

A

$y(t) = -\cfrac{1}{4} \cos 5t + \cfrac{19}{105}\sin 5t + \cfrac{1}{4} \cos 3t + \cfrac{1}{21} \sin 2t$

B

$y(t) = \cfrac{1}{5}\sin 5t + \cfrac{1}{16} \cos 3t + \cfrac{4}{21} \sin 2t$

C

$y(t) = -\cfrac{1}{16} \cos 5t - \cfrac{8}{105}\sin 5t + \cfrac{1}{16} \cos 3t + \cfrac{4}{21} \sin 2t$

D

None of the above