Answer
$y=e^{-2x}$ is a solution
Work Step by Step
First take the derivative of y to find y'
$y= e^{-2x}$
$y'= -2e^{-2x}$
Then substitute y and y' into the differential equation
$ 3(-2e^{-2x} ) + 5(e^{-2x} )=-e^{-2x}$
$-6e^{-2x} +5e^{-2x} = -e^{-2x}$
$-e^{-2x} = -e^{-2x} $
The solution checks with the differential equation
so $y=e^{-2x}$ is a solution.