1. The problem statement, all variables and given/known data Find the general solution for the equation (x - 1)y'' - xy' + y = sin(x), x > 1 Given that y_1(x) = e^x satisfies the associated homogeneous equation. 2. Relevant equations y_2 = v_2(x) * y_1 3. The attempt at a solution I read http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx and attempted to replicate its method several times and I am attaching my latest attempt. The website I linked to says "Note that upon simplifying the only terms remaining are those involving the derivatives of v. The term involving v drops out. If you’ve done all of your work correctly this should always happen." but I have a term involving v that did not drop out. Also, am I supposed to ignore sin(x) or not? Based on the way the question is phrased, I'd now say I should of ignored it (please tell me if I am correct in saying this) but it doesn't matter for what I am questioning. By the way, this thread is just about the reduction of order part. (The next step is variation of parameters but I haven't gotten there yet.) Any help would be greatly appreciated! Thanks in advance!