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

question 60

Multiple Choice

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

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

---

Definitions:

Labor Rate Variance

The difference between the actual cost of labor and the standard or expected cost, often analyzed in cost accounting.

Labor Efficiency Variance

Labor Efficiency Variance measures the difference between the actual hours worked and the standard hours expected for the work performed.

Direct Labor Wage

The compensation workers receive for directly contributing to the manufacturing or production of goods, usually an hourly wage or per unit produced rate.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the standard cost allocated for the actual production level.