When determining a particular solution to a differential equation, one of the necessary steps is to ask the "homogeneous question" aka Does any term in yp solve the homogeneous equation for this problem. When it does, I know that it is necessary to multiple by t. My question is, do I multiply yp by T and then derive, or do I derive and then multiply by T? For example, A cos(t) solves the homogeneous equation for a problem I'm working on. Do I derive it first: y(p) = Acos(T) Y'(p) = -Asin(T) Y''(p) = -Acos(T) And then multiply each of those by T, or do I multiply by T first and then derive? It makes a big difference!