The Solution of the Initial Value Problem $\begin{array} { l } \frac { d x } { d t } = 10 x - 5 y \\\frac { d y } { d t } = 8 x - 12 y \\x ( 0 ) = 2 , y ( 0 ) = 1\end{array}$

question 12

Multiple Choice

The solution of the initial value problem $\begin{array} { l } \frac { d x } { d t } = 10 x - 5 y \\\frac { d y } { d t } = 8 x - 12 y \\x ( 0 ) = 2 , y ( 0 ) = 1\end{array}$ is

• A) \(x = \left( 35 e ^ { 8 t } - e ^ { - 10 t } \right) / 18 , y = \left( 7 e ^ { 8 t } + 2 e ^ { - 10 t } \right) / 9\)
• B) \(x = \left( 35 e ^ { 8 t } + e ^ { - 10 t } \right) / 18 , y = \left( 7 e ^ { 8 t } + 2 e ^ { - 10 t } \right) / 9\)
• C) \(x = \left( 35 e ^ { 8 t } + e ^ { - 10 t } \right) / 9 , y = \left( 7 e ^ { 8 t } + 2 e ^ { - 10 t } \right) / 9\)
• D) \(x = \left( 35 e ^ { 8 t } - e ^ { - 10 t } \right) / 9 , y = \left( 7 e ^ { 8 t } - 2 e ^ { - 10 t } \right) / 9\)
• E) \(x = \left( 35 e ^ { 8 t } + e ^ { - 10 t } \right) / 18 , y = \left( 7 e ^ { 8 t } - 2 e ^ { - 10 t } \right) / 9\)

---

Definitions:

Different Interests

Diverse or varying priorities and desires among individuals or groups in a negotiation or decision-making process .

Surface

The outermost layer or boundary of an object or the superficial aspect of something as opposed to its essence.

Benefit

An advantage or profit gained from something, often used in the context of employment, insurance, or social welfare.

Logrolling

A practice in negotiation or politics where two parties agree to support each other's proposals or interests.