Judicious guess for the solution of differential equation $y''-2y'+5y=2(\cos t)^2 e^t$ I want to find the solutions of the differential equation: $y''-2y'+5y=2(\cos t)^2 e^t$.
I want to do this with the judicious guessing method and therefore I want to write the right part of the differential equations as the imaginary part of a something. How can I do this?

Hint: $(\cos t)^2 = (1 + \cos(2 t))/2$.
