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Differential Equations

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Moderate

Second Order Homogeneous - All Solutions

DIFFEQ-LCIQLL

Find all solutions to the following initial value problem:

$$x''-4x'+13x=0,\ x(0)=1$$

A

$x(t)=c_1e^{2t}\cos(3t)+c_2e^{2t}\sin(3t)$, where $c_1$ and $c_2$ can be any real numbers.

B

$x(t)=e^{2t}\cos(3t)+ce^{2t}\sin(3t)$, where $c$ can be any real number.

C

$x(t)=e^{2t}\cos(3t)$.

D

$x(t)=e^{2t}\cos(3t)-e^{2t}\sin(3t)$.