Solve the first-order linear ODE: y′+2y=e−2xy' + 2y = e^{-2x}y′+2y=e−2x.
y=xe−2x+Ce−2xy = x e^{-2x} + Ce^{-2x}y=xe−2x+Ce−2x
y=e−2x+Ce−2xy = e^{-2x} + Ce^{-2x}y=e−2x+Ce−2x
y=2e−2x+Cy = 2e^{-2x} + Cy=2e−2x+C
y=e2x+Cy = e^{2x} + Cy=e2x+C