The solution to the differential equation $\frac { d y } { d x } = - 3 y$ satisfying the boundary condition y = 3 when x = 0 is

A) $y = e ^ { 3 x } + 3$
B) $y = e ^ { - 3 x } + 3$
C) $y = 3 e ^ { 3 x }$
D) $y = - 3 e ^ { - 3 x }$
E) $y = 3 e ^ { - 3 x }$

Question

The solution to the differential equation $\frac { d y } { d x } = - 3 y$ satisfying the boundary condition y = 3 when x = 0 is

A) $y = e ^ { 3 x } + 3$
B) $y = e ^ { - 3 x } + 3$
C) $y = 3 e ^ { 3 x }$
D) $y = - 3 e ^ { - 3 x }$
E) $y = 3 e ^ { - 3 x }$

Quizplus · Accepted Answer

The differential equation $\frac { d y } { d x } = - 3 y$ is a first-order linear differential equation. Its general solution is of the form $y = C e ^ { - 3 x }$, where $C$ is a constant. Applying the boundary condition $y(0) = 3$, we find $C = 3$, making the solution $y = 3 e ^ { - 3 x }$.

The Solution to the Differential Equation dydx=−3y\frac { d y } { d x } = - 3 ydxdy​=−3y

The Solution to the Differential Equation $\frac { d y } { d x } = - 3 y$