Question

Find all values of m so that the function
y = emx
is a solution of the given differential equation. (Enter your answers as a comma-separated list.)
y' + 3y = 0

Answer 1

Where are you having trouble?

Answer 2

Idk how to start. Do I integrate both sides first?

Answer 3

or do I integrate \[y=e ^{mx}\] and then plug it in in the equation \[y \prime + 3y = 0\] ?

Answer 4

y'+3y=0
(D+3)y=0
D+3=0
D=-3
y=e^-3x
Source: http://www.mathskey.com/question2answer/

Answer 5

or dy/dx+3y=0
dy/dx=-3y
dy/y = -3dx
Integrate both sides
lny =-3x
y =e^-3x+c
Source: http://www.mathskey.com/question2answer/

Answer 6

\[y = e^{mx}\]What is the derivative of this?
\[y'=. . .%me^{mx}
\]

Answer 7

then plug \(y\) and \(y'\) into \[y' + 3y = 0\] and solve for m

Answer 8

Hint: (factor, and assume \(e^{mx}\neq0\))