The Solution of the System of Differential Equations $\begin{array} { l } \frac { d x } { d t } = - 6 x + 5 y \\\frac { d y } { d t } = - 5 x + 4 y \\x ( 0 ) = 1 / 3 , y ( 0 ) = 0\end{array}$

question 18

Multiple Choice

The solution of the system of differential equations $\begin{array} { l } \frac { d x } { d t } = - 6 x + 5 y \\\frac { d y } { d t } = - 5 x + 4 y \\x ( 0 ) = 1 / 3 , y ( 0 ) = 0\end{array}$ is

• A) \(x = \left( e ^ { t } - 5 t e ^ { t } \right) / 3 , y = - 5 t e ^ { t } / 3\)
• B) \(x = \left( e ^ { - t } - t e ^ { - t } \right) / 3 , y = - t e ^ { - t } / 3\)
• C) \(x = \left( e ^ { - t } + t e ^ { - t } \right) / 3 , y = t e ^ { - t } / 3\)
• D) \(x = \left( e ^ { - t } + 5 t e ^ { - t } \right) / 3 , y = 5 t e ^ { - t } / 3\)
• E) \(x = \left( e ^ { - t } - 5 t e ^ { - t } \right) / 3 , y = - 5 t e ^ { - t } / 3\)

---

Definitions:

Opportunity Cost

Foregoing the chance for potential earnings from other routes when one is selected.

Bushels of Corn

A unit of measurement used in agriculture, particularly in the United States, to quantify volumes of corn production and trade.

Opportunity Cost

The price paid for not choosing the next most favorable option when a decision is made.

Absolute Advantage

A situation in which a person or economy can produce more of a good with the same amount of resources as someone else.