Solve the first-order linear ODE: y′+y=exy' + y = e^xy′+y=ex.
y=12ex+Ce−xy = \frac{1}{2}e^x + Ce^{-x}y=21ex+Ce−x
y=ex+Ce−xy = e^x + Ce^{-x}y=ex+Ce−x
y=12e2x+Cy = \frac{1}{2}e^{2x} + Cy=21e2x+C
y=ex+Cy = e^x + Cy=ex+C