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Differential Equations

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Moderate

Nonhomogeneous 3111

DIFFEQ-65GJJL

Determine the form of the particular solution of the system:

$$X'=\left(\begin{array}{cc} 5 & 3 \\\ -1 & 1 \end{array}\right)X+\left(\begin{array}{c}-2e^{2t}+1 \\\ e^{2t}-5t+17\end{array}\right)$$

A

$X_{p}=\left(\begin{array}{c}a_{2} \\\ b_{2}\end{array}\right)e^{2t}+\left(\begin{array}{c}a_{1} \\\ b_{1}\end{array}\right)$

B

$X_{p}=\left(\begin{array}{c}a_{3} \\\ b_{3}\end{array}\right)e^{2t}+\left(\begin{array}{c}a_{2} \\\ b_{2}\end{array}\right)t+\left(\begin{array}{c}a_{1} \\\ b_{1}\end{array}\right)$

C

$X_{p}=\left(\begin{array}{c}a_{2} \\\ b_{2}\end{array}\right)te^{2t}+\left(\begin{array}{c}a_{1} \\\ b_{1}\end{array}\right)t$

D

$X_{p}=\left(\begin{array}{c}a_{4} \\\ b_{4}\end{array}\right)te^{2t}+\left(\begin{array}{c}a_{3} \\\ b_{3}\end{array}\right)e^{2t}+\left(\begin{array}{c}a_{2} \\\ b_{2}\end{array}\right)t+\left(\begin{array}{c}a_{1} \\\ b_{1}\end{array}\right)$

E

None of the above