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Differential Equations

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Moderate

2nd-Order Inhomogeneous - Sin(t)

DIFFEQ-V12ES8

Consider the following ordinary differential equation:

$$x''+3x'+x=\sin{(t)}$$

Choose the BEST answer.

A

Every solution $x$ satisfies $\lim_{t\rightarrow\infty}x(t)=0$.

B

Every solution $x$ satisfies $\lim_{t\rightarrow\infty}x(t)=\infty$.

C

Every solution $x$ oscillates infinitely often as $t\rightarrow\infty$.

D

Some solutions $x$ satisfy $\lim_{t\rightarrow\infty}x(t)=0$, while
others oscillate infinitely often as $t\rightarrow\infty$.