Which of the following functions are solutions to the differential equation $\frac { d y } { d x } = \frac { y } { 3 }$ ? (Mark all correct answers.)
A) $y = \sin ( 3 x ) + \cos ( 3 x )$
B) $y = 3 \cos x - \sin x$
C) $y = e ^ { x / 3 }$
D) $y = e ^ { - x / 3 }$

Question

Quizplus · Accepted Answer

The differential equation $\frac{dy}{dx} = \frac{y}{3}$ is a first-order linear differential equation with the solution of the form $y = Ce^{x/3}$, where $C$ is a constant. Thus, $y = e^{x/3}$ is a solution.

Which of the Following Functions Are Solutions to the Differential dydx=y3\frac { d y } { d x } = \frac { y } { 3 }dxdy​=3y​

Which of the Following Functions Are Solutions to the Differential $\frac { d y } { d x } = \frac { y } { 3 }$