Answer
The general solution satisfies the differential equation and the particular solution is $ y=3e^{-2x} $
Work Step by Step
Begin by finding the derivative of y.
$y=Ce^{-2x}$
$y'= -2Ce^{-2x}$
Then substitute y and y' into the differential equation.
$y' +2y=0$
$(-2Ce^{-2x}) +2(Ce^{-2x}) =0 $
$0=0$
The general solution satisfies the differential equation.
Now, to find the particular solution.
y=3, when x=0
$3=Ce^{-2(0)}$
$3=C$
Substitute C into the Solution to get the particular solution
$y=3e^{-2x}$
