Solve the Initial-Value Problem $$y ^ { tt } + 3 y ^ { t } - 4 y = 0 , y ( 0 ) = 2 , y ^ { t } ( 0 ) = 1$$

question 59

Multiple Choice

Solve the initial-value problem. $$y ^ { tt } + 3 y ^ { t } - 4 y = 0 , y ( 0 ) = 2 , y ^ { t } ( 0 ) = 1$$

• A)\(y = e ^ { 2 x } + \frac { 1 } { 5 } e ^ { - 2 x }\)
• B) \(y = \frac { 9 } { 5 } e ^ { x } + \frac { 1 } { 5 } e ^ { - 4 x }\)
• C) \(y = \frac { 1 } { 5 } e ^ { 2 x } + \frac { 9 } { 5 } e ^ { - 2 x }\)
• D) \(y = e ^ { x } + \frac { 1 } { 5 } e ^ { - 3 x }\)
• E) None of these

---

Definitions:

Menarche

The first occurrence of menstruation in a female, marking the onset of reproductive capability.

Kohlberg's Theory

A theory of moral development proposed by Lawrence Kohlberg, which suggests that individuals progress through a series of stages in understanding of right and wrong.

Moral Development

The process through which individuals develop proper attitudes and behaviors towards other people in society, based on social norms, cultural practices, and laws.

Cultural Disparities

Differences in cultural resources and status that exist within and between societies, often reflecting inequalities in access to wealth, healthcare, education, and opportunities.