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:

Population Mean

The average value of a set of characteristics for an entire population.

Alpha

A threshold value in hypothesis testing that determines the level of significance, usually set to 0.05 or 0.01.

Type I Error

An error in hypothesis testing that occurs when the null hypothesis is wrongly rejected, falsely indicating a significant result.

Two-tailed Hypothesis

A hypothesis test that considers both directions of an effect, allowing for the possibility of difference in either direction from the null hypothesis.