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Differential Equations

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Second Order Homogeneous IVP

DIFFEQ-GLCFS2

Solve the initial value problem:

$$x''+9x=0,\ x(0)=1,\ x'(0)=1$$

A

$x(t)=c_1\cos(3t)+c_2\sin(3t)$, where $c_1$ and $c_2$ can be any real numbers.

B

$x(t)=2\cos(3t)-\cfrac{1}{3}\sin(3t)$

C

$x(t)=\cos(3t)+\cfrac{2}{3}\sin(3t)$

D

$x(t)=\cos(3t)+\cfrac{1}{3}\sin(3t)$