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

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Definitions:

Network Diagram

A visual representation of a project's activities and their sequence, showing the path from start to finish, including dependencies.

Cycle Time

The total time from the beginning to the end of a process, which includes both processing and waiting times.

Maximum Cycle Time

The longest duration permitted for completing one cycle of a production process, defining the upper limit of process efficiency.

Efficiency

The ratio of output generated to the input used, illustrating how well resources are being utilized to produce desired results.