Solve the first-order linear ODE: y′−y=e2xy' - y = e^{2x}y′−y=e2x.
y=2e2x+Cy = 2e^{2x} + Cy=2e2x+C
y=e2x+Cexy = e^{2x} + Ce^xy=e2x+Cex
y=e2x−Cexy = e^{2x} - Ce^xy=e2x−Cex
y=ex+Cy = e^x + Cy=ex+C