A particular solution of $\mathbf { X } ^ { \prime } = \left( \begin{array} { c c }
0 & 1 \
- 1 & 0
\end{array} \right) \mathbf { X } + \left( \begin{array} { c }
1 \
e ^ { t }
\end{array} \right)$ is
A) $\left( \begin{array} { c }
e ^ { t } / 2 \
- e ^ { t } / 2 + 1
\end{array} \right)$
B) $\left( \begin{array} { c }
- e ^ { t } / 2 \
e ^ { t } / 2 - 1
\end{array} \right)$
C) $\left( \begin{array} { c }
e ^ { t } / 2 \
- e ^ { t } / 2 - 1
\end{array} \right)$
D) $\left( \begin{array} { c }
e ^ { t } / 2 \
e ^ { t } / 2 + 1
\end{array} \right)$
E) $\left( \begin{array} { c }
e ^ { t } / 2 \
e ^ { t } / 2 - 1
\end{array} \right)$

Question

A particular solution of $\mathbf { X } ^ { \prime } = \left( \begin{array} { c c } 
0 & 1 \
- 1 & 0
\end{array} \right) \mathbf { X } + \left( \begin{array} { c } 
1 \
e ^ { t }
\end{array} \right)$ is
A) $\left( \begin{array} { c } 
e ^ { t } / 2 \
- e ^ { t } / 2 + 1
\end{array} \right)$
B) $\left( \begin{array} { c } 
- e ^ { t } / 2 \
e ^ { t } / 2 - 1
\end{array} \right)$
C) $\left( \begin{array} { c } 
e ^ { t } / 2 \
- e ^ { t } / 2 - 1
\end{array} \right)$
D) $\left( \begin{array} { c } 
e ^ { t } / 2 \
e ^ { t } / 2 + 1
\end{array} \right)$
E) $\left( \begin{array} { c } 
e ^ { t } / 2 \
e ^ { t } / 2 - 1
\end{array} \right)$

Quizplus · Accepted Answer

The Answer of A particular solution of $\mathbf { X } ^ { \prime } = \left( \begin{array} { c c } 
0 & 1 \
- 1 & 0
\end{array} \right) \mathbf { X } + \left( \begin{array} { c } 
1 \
e ^ { t }
\end{array} \right)$ is
A) $\left( \begin{array} { c } 
e ^ { t } / 2 \
- e ^ { t } / 2 + 1
\end{array} \right)$
B) $\left( \begin{array} { c } 
- e ^ { t } / 2 \
e ^ { t } / 2 - 1
\end{array} \right)$
C) $\left( \begin{array} { c } 
e ^ { t } / 2 \
- e ^ { t } / 2 - 1
\end{array} \right)$
D) $\left( \begin{array} { c } 
e ^ { t } / 2 \
e ^ { t } / 2 + 1
\end{array} \right)$
E) $\left( \begin{array} { c } 
e ^ { t } / 2 \
e ^ { t } / 2 - 1
\end{array} \right)$

A Particular Solution Of Is A) (et/2−et/2+1)\left( \begin{array} { c } e ^ { t } / 2 \\- e ^ { t } / 2 + 1\end{array} \right)(et/2−et/2+1​)

A Particular Solution Of Is
A) $\left( \begin{array} { c } e ^ { t } / 2 \\- e ^ { t } / 2 + 1\end{array} \right)$