Solve the first-order linear ODE: y′+4y=e−xy' + 4y = e^{-x}y′+4y=e−x.
y=13e−x+Ce−4xy = \frac{1}{3}e^{-x} + Ce^{-4x}y=31e−x+Ce−4x
y=e−x+Ce−4xy = e^{-x} + Ce^{-4x}y=e−x+Ce−4x
y=13ex+Cy = \frac{1}{3}e^x + Cy=31ex+C
y=e−4x+Cy = e^{-4x} + Cy=e−4x+C