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Differential Equations

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General Solution to a Forced Oscillator

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Consider the forced oscillator:

$$\begin{equation} y'' + 10 y = \sqrt{3} \cos 4t \end{equation}$$

The general solution to this differential equation is:

A

$y(t) = - \cfrac{\sqrt{3}}{6} \cos 4t$

B

$y(t) = A \cos \sqrt{10} t + B \sin \sqrt{10} t$

C

$y(t) = \cos \sqrt{10} t + \sin \sqrt{10} t - \cfrac{\sqrt{3}}{6} \cos 4t$

D

$y(t) = A \cos \sqrt{10} t + B \sin \sqrt{10} t - \cfrac{\sqrt{3}}{6} \cos 4t$