Differential Equations

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Moderate

Identifing the Particular Solution to the Nonhomogeneous System

DIFFEQ-BGE1AT

Which is a correct form of a particular solution to the nonhomogeneous system:

$$X'=\left(\begin{array}{cc}2 & 1 \\\ 0 & 1 \end{array}\right)X+\left(\begin{array}{c}e^{t} \\\ t+1\end{array}\right)$$

A

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

B

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

C

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

D

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

E

None of the above