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

question 24

Multiple Choice

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

• A) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t - 16\)
• B) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } + 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t + 16\)
• C) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { t } + c _ { 2 } t e ^ { t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { t } + c _ { 2 } t e ^ { t } - 5 t + 16\)
• D) \(x = \left( c _ { 1 } - c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t + 16\)
• E) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t + 16\)

Understand the constitutional arguments and political thought influencing colonial opposition to British legislation.

Assess the economic effects of British legislation and warfare on the colonial economy and the mercantile system.

Appreciate the complexities of colonial allegiance and identity in relation to both the British crown and Parliament.

Evaluate the significance of public rituals, grassroots movements, and the role of social class in the resistance efforts.

---

Definitions:

Psychological Thought

The theories, principles, and concepts that form the basis of psychology as a scientific discipline.

Functionalism

A theoretical framework in sociology and anthropology that explains social institutions and structures by the role they play in society.

Adapt to Environment

The process by which organisms adjust and change in response to their external environment.

Psychology

The scientific study of the mind and behavior, encompassing various aspects of conscious and unconscious experience.