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

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Definitions:

Implied Authority

Authority of an agent that is not explicitly stated but is deemed necessary to carry out express authority.

Duty of Performance

An obligation of a party in a contract to fulfill the terms and conditions as agreed within the contract.

Reasonable Skill

A term used to describe the level of competence that a professional or practitioner is expected to display in their field, often used in legal contexts to establish standards for professional services.

Fiduciary

A person who holds a position of trust, required to act for the benefit of another party with respect to specific duties.