Use the method of undetermined coefficients to find solution

Use the method of undetermined coefficients to find solutions to the following non-homogeneous, constant coefficient, linear ODEs.

y?? + 4y? = t

Solution

Auxialary equation is m^2 +4m =0

Solution is m =-2i, 2i

Hence general solution is

y = Acos2t + B sin 2t

Particualr solution of y =   = 1/4 ( 1-D^2+...)t

= t/4

Hence

y = A cos 2t+ Bsin 2t+t/4