Question

Find all values of m so that the function

y = e^mx
is a solution of the given differential equation. y' + 9y = 0

Answer 1

Hello,

y=e^(mx)
y'=m*e^(mx)

0=y'+9y=m*e^(mx)+9*e^(mx)
==> e^(mx)*(m+9)=0
This must be exact for every value of ,so
m=-9