**1. The problem statement, all variables and given/known data**

Given the equation 5y''(t)−y'(t)+7y(t) = 3te

^{4t}cos2t + t

^{2}e

^{t}+ 4t

^{3}e

^{2t}sin4t − (2/3)e

^{t}+ 9e

^{2t}cos4t, if the Method of Undetermined Coefficients and the Principle of Superposition are used to find a particular solution, what is the minimum number of nonhomogeneous equations which must be solved?

**2. Relevant equations**

The answer is 3. I believe this is because each individual, unique term on the right side has to be solved separately, and then each of these solutions are summed to find the general solution to the diff eq. Even though there are 5 separate terms on the right side, the e

^{t}terms can be grouped and solved at once, and since cost + sint = 1, I'm guessing the sin4t and cos4t terms can be grouped as well. Am I way off?

Thanks for the help, hopefully this is a quickie.