Use the Method of Undetermined Coefficients to find a particular solution Y of the third order non-homogeneous linear differential equation y''' − y'' + y' − y = 4 (e^t + e^−t ) Hint — Recall that Y =...

Use the Method of Undetermined Coefficients to find a particular solution Y of the third order non-homogeneous linear differential equation

y''' − y'' + y' − y = 4 (e^t + e^−t )

Hint — Recall that Y = Y1 + Y2, where Y1 and Y2 are particular solutions of the simpler equations

y''' − y'' + y' − y = 4 e^t ,

y''' − y'' + y' − y = 4 e^−t ,

respectively.