I am looking to solve for the above nonhomogeneous ODE. I know how to find the general solution for the reduced equation of the homogeneous form, that is, $ $ y” – 4y’ – 5y = 0.$ $

The characteristic equation is $ r^{2} – 4r – 5 = 0$ , which gives two real and distinct roots $ r=-1,5$ .

So the complementary solution is $ y_{c}=c_{1}e^{5x} + c_{2}e^{-x}$ .

Now I am looking to guess the particular on the right-hand side but I am not sure about how to do that in order to find the general solution of the above nonhomogenous ODE.