Solve the differential equation.
-$$e ^ { x } \frac { d y } { d x } + 3 e ^ { x } y = 2 , x 0$$
A) $y = e ^ { - 3 x } + C e ^ { - x } , x 0$
B) $y = e ^ { - x } + e ^ { - 3 x } , x 0$
C) $y = e ^ { - x } + C e ^ { - 3 x } , x 0$
D) $y = e ^ { x } + C e ^ { - 3 x } , x 0$

Question

Solve the differential equation.
-$$e ^ { x } \frac { d y } { d x } + 3 e ^ { x } y = 2 , x > 0$$
A) $y = e ^ { - 3 x } + C e ^ { - x } , x > 0$
B) $y = e ^ { - x } + e ^ { - 3 x } , x > 0$
C) $y = e ^ { - x } + C e ^ { - 3 x } , x > 0$
D) $y = e ^ { x } + C e ^ { - 3 x } , x > 0$

Quizplus · Accepted Answer

The given differential equation is a first-order linear differential equation. The integrating factor is $e^{\int 3 dx} = e^{3x}$. Multiplying through by the integrating factor and solving gives the solution $y = e^{-x} + Ce^{-3x}$.

Solve the Differential Equation exdydx+3exy=2,x>0e ^ { x } \frac { d y } { d x } + 3 e ^ { x } y = 2 , x > 0exdxdy​+3exy=2,x>0

Solve the Differential Equation $e ^ { x } \frac { d y } { d x } + 3 e ^ { x } y = 2 , x > 0$