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

question 16

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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