The Particular Solution Of Is
A) $\left( \begin{array} { c } 2 t e ^ { t } / 5 + 3 e ^ { t } \\- 2 t e ^ { t } / 5 + 2 e ^ { t }\end{array} \right)$

question 4

Multiple Choice

The particular solution of $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 2 & 3 \\2 & 1\end{array} \right) \mathbf { X } + \left( \begin{array} { c } e ^ { - t } \\0\end{array} \right)$ is

• A) \(\left( \begin{array} { c }
• 2 t e ^ { t } / 5 + 3 e ^ { t } \\
• - 2 t e ^ { t } / 5 + 2 e ^ { t }
• \end{array} \right)\)
• B) \(\left( \begin{array} { c }
• 2 t e ^ { - t } / 5 + 3 e ^ { - t } \\
• - 2 t e ^ { - t } / 5 + 2 e ^ { - t }
• \end{array} \right)\)
• C) \(\left( \begin{array} { c }
• 2 t e ^ { - t } / 5 - 3 e ^ { - t } \\
• - 2 t e ^ { - t } / 5 - 2 e ^ { - t }
• \end{array} \right)\)
• D) \(\left( \begin{array} { c }
• 2 t e ^ { t } / 5 - 3 e ^ { t } \\
• - 2 t e ^ { t } / 5 - 2 e ^ { t }
• \end{array} \right)\)
• E) none of the above

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Definitions:

Stock Dividends Distributable

A portion of a company's earnings allocated to shareholders in the form of additional shares, rather than cash, typically at a fixed rate.

Retained Earnings

The portion of net income that is retained by a company rather than distributed to its shareholders as dividends.

Dividends Declared

Profit distributed by a company to its shareholders, typically in the form of cash or additional stock, based on the number of shares owned.

Stock Split

A stock split is an action taken by a company to divide its existing shares into multiple ones to boost the liquidity of the shares, without changing the overall value of shareholders' equity.