1. The problem statement, all variables and given/known data Solve by variation of parameters: y" + 3y' + 2y = sinex 2. Relevant equations Finding the complimentary yields: yc = c1e-x + c2e-2x 3. The attempt at a solution I set up the Wronskians and got: μ1 = ∫e-2xsin(ex)dx μ2 = -∫e-xsin(ex)dx The problem is that I have no idea how to integrate sin(ex). I tried subbing u = e-x du = -e-x for μ1 => ∫-u du sin(u-1) Integration by parts either attempts to integrate sin(u-1) or endlessly integrates u without repeat. That failed, so I tried just integrating by parts of μ1; it took 2 repetitions to get: μ1 = -½e-2xsin(ex) - ½e-xcos(ex) + ∫½sin(ex)dx I thought it might work if I get -ex∫½sin(ex)] in μ2 μ2 = e-xsin(ex) - ∫cos(ex)dx Going further into the integration by parts just adds more complications, such as adding "x" as a term as well as going into higher powers of ex. I can't express the integral as a series; that's next chapter and not covered on the mid-term in a few days (I'm currently hoping the mid-term doesn't have this problem).