Solve the first-order linear ODE: y′+3y=exy' + 3y = e^xy′+3y=ex.
y=14ex+Ce−3xy = \frac{1}{4}e^x + Ce^{-3x}y=41ex+Ce−3x
y=ex+Ce−3xy = e^x + Ce^{-3x}y=ex+Ce−3x
y=14e4x+Cy = \frac{1}{4}e^{4x} + Cy=41e4x+C
y=e−3x+Cy = e^{-3x} + Cy=e−3x+C