Find the general solution to the differential equation dudt+u=4e−tu3\frac{du}{dt} + u = 4e^{-t}u^3dtdu+u=4e−tu3.
u−2=8t+Ce2tu^{-2} = 8t + Ce^{2t}u−2=8t+Ce2t
u−2=8te2t+Cu^{-2} = 8te^{2t} + Cu−2=8te2t+C
u2=8t+Ce2tu^2 = 8t + Ce^{2t}u2=8t+Ce2t
u−2=4e−2t+Cu^{-2} = 4e^{-2t} + Cu−2=4e−2t+C