Higher order non-homogeneous linear diff equations:

(Method of Undetermined Coefficients)

1. Find the general solution of the diff equations.

a.   \( y'''+2y''-4y'-8y=5e^{3t} \) solution

b.  \( y^{(4)}+4y''=3\sin(2t) \)   solution

2. SET UP the correct form for the particular solution, \( y_p(t)\). solution

a.  \( y^{(4)}-3y'''+2y''=5e^{t}+7t \)

b.  \( y'''-3y''=\cosh(3t)-5t^2 \)

3 . SET UP the correct form for the particular solution, \( y_p(t)\). Note that \(D=\frac{d}{dt}.\)

a.(i) \(y''-y= 2e^{t} \)   (ii) \(y'''-y''-6y'= 7te^{-2t} \)   solution

b.(i) \(y'''+4y' = 3te^{t} +3\sin(2t)\)   (ii) \(D^2(D+1)^3[y] = 5t-7+4e^{-t} \)   solution