Question

Find all values of m so that the function

y = e^mx is a solution of the given differential equation. (Enter your answers as a comma-separated list.)
y' + 3y = 0

Answer 1

First, solve the differential equation by integrating it:

y' + 3y = 0
dy/dx + 3y = 0
dy/dx = -3y
dy = -3ydx
-∫dy/3y = ∫dx
-(1/3)lny = x
e^(lny) = e^(-3x)
y = e^(-3x)

Therefore, that means that the m is equal to -3.