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

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.

Correct Answer:

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