Find the Integrating Factor, the General Solution, and the Particular $y ^ { \prime }$

question 52

Multiple Choice

Find the integrating factor, the general solution, and the particular solution satisfying the initial condition. $y ^ { \prime }$ - 4y = -2 $e ^ { 2 t }$ ; y(0) = -1

• A) integrating factor: \(e ^ { - 4 t }\)
• General solution: \(y = - e ^ { - 2 t } + C ^ { e ^ { 4 t } }\)
• Particular solution: y = - \(e ^ { - 2 t }\) - 2 \(e ^ { 4 t }\)
• B) integrating factor: \(e ^ { - 4 t }\)
• General solution: y = \(e ^ { 2 t }\) + C \(e ^ { 4 t }\)
• Particular solution: y = \(e ^ { 2 t }\) - 2 \(e ^ { 4 t }\)
• C) integrating factor: \(e ^ { 4 t }\)
• General solution: y = -2t + C \(e ^ { 4 t }\)
• Particular solution: y = -2t - \(e ^ { 4 t }\)
• D) integrating factor: \(e ^ { 4 t }\)
• General solution: y = \(\frac { 1 } { 3 }\) \(e ^ { 6 t }\) + C \(e ^ { 4 t }\)
• Particular solution: y = \(\frac { 1 } { 3 }\) \(e ^ { 6 t }\) - \(\frac { 4 } { 3 }\) \(e ^ { 4 t }\)
• Solve the equation using an integrating factor.

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