1. The problem statement, all variables and given/known data This isn't a problem, I'm just obsessed with analyzing a trig/exp equation algebraically instead of with a calculator. 8*sin(t) - 16*cos(t) = 9*exp(-t/2) 2. Relevant equations See part (1.) above... 3. The attempt at a solution I tried converting the exp part into a Fourier series; if you graph the equation, this method recommends itself due to the multiple solutions. I didn't have much success with this method, though, since the first term in the Fourier series contains two exp terms. In addition, the Fourier series requires the definition of an integrable "period", and I wouldn't know what to do for that. I also tried converting the sine and cosine terms into exp terms with complex arguments, but then I've got imaginary numbers all over the place, and I already know the answer isn't complex from the solution obtained by calculator, which was verified graphically. Any recommendations would be grand.