Solve the equation using an integrating factor.
-$y ^ { \prime } - 3 y = 6$ , t 0
A) y = C $e ^ { 3 t }$ + C
B) y = C $e ^ { 3 t }$
C) y = C $e ^ { 3 t }$ - 2
D) y = C $e ^ { - 3 t }$

Question

Solve the equation using an integrating factor. 
-$y ^ { \prime } - 3 y = 6$ , t > 0
A) y = C $e ^ { 3 t }$ + C
B) y = C $e ^ { 3 t }$
C) y = C $e ^ { 3 t }$ - 2
D) y = C $e ^ { - 3 t }$

Quizplus · Accepted Answer

The integrating factor is $e^{\int -3 dt} = e^{-3t}$. Multiplying through by this factor and solving gives the solution $y = Ce^{3t} - 2$.

Solve the Equation Using an Integrating Factor y′−3y=6y ^ { \prime } - 3 y = 6y′−3y=6

Solve the Equation Using an Integrating Factor $y ^ { \prime } - 3 y = 6$