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Differential Equations

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Moderate

Second Order Homogeneous - $x'(0)=2$

DIFFEQ-FONUN1

Solve the initial value problem:

$$x''+2x'+2x=0,\ x(0)=1,\ x'(0)=2$$

A

$x(t)=c_1e^{t}\cos(t)+c_2e^{t}\sin(t)$

B

$x(t)=e^t\cos(t)+3e^t\sin(t)$

C

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

D

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