?

Differential Equations

Free Version

Upgrade subject to access all content

Difficult

Finding General Solution to Nonhomogeneous System, -5 and 2

DIFFEQ-VEXP18

Which is a general solution to the system of nonhomogeneous differential equations:

$$X'=\left(\begin{array}{cc}0 & -1 \\\ 1 & 0 \end{array}\right)X+\left(\begin{array}{c}-5 \\\ 2 \end{array}\right)$$

A

$X=c_{1}\left(\begin{array}{c}\cos t \\\ \sin t \end{array}\right)+c_{2}\left(\begin{array}{c}\sin t \\\ -\cos t \end{array}\right)+\left(\begin{array}{c} -2 \\\ -5 \end{array}\right)$

B

$X=c_{1}\left(\begin{array}{c}\cos t \\\ \sin t \end{array}\right)+c_{2}\left(\begin{array}{c}\sin t \\\ -\cos t \end{array}\right)+\left(\begin{array}{c} 2 \\\ 5 \end{array}\right)$

C

$X=c_{1}\left(\begin{array}{c}\cos t \\\ -\sin t \end{array}\right)+c_{2}\left(\begin{array}{c}\sin t \\\ \cos t \end{array}\right)+\left(\begin{array}{c} -2 \\\ -5 \end{array}\right)$

D

$X=c_{1}\left(\begin{array}{c}0 \\\ -1 \end{array}\right) \cos t+c_{2}\left(\begin{array}{c} 1 \\\ 0 \end{array}\right)+\left(\begin{array}{c} -5 \\\ 2 \end{array}\right)$

E

None of the above