## Calculus 10th Edition

The general solution satisfies the differential equation and the particular solution is $y=3e^{-2x}$
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 $y=3e^{-2x}$