Use the Method of Variation of Parameters to find the general solution y(t) of the third order non-homogeneous linear differential equation y''' − 3y'' + 3y' − y = t. Hint — The characteristic...

Use the Method of Variation of Parameters to find the general solution y(t) of the third order non-homogeneous linear differential equation

y''' − 3y'' + 3y' − y = t.

Hint — The characteristic equation of the associated homogeneous differential equation is

r^3 − 3r^2 + 3r − 1 = (r − 1)^3 = 0.