In applying the usual formula for y'+py=q with u=e∫p and y=(∫uq +C)/u, the results of the indefinite integral to calculate u is without a constant. Why is this? The result is not the same. For example, suppose I take the problem dy/dx +y = x*exp(-x). Then, in the usual manner, I get a nice exp(-x)*(x2/2 +C). But if I were to put constants in for the integration factor, I get exp(-x)*(C1x2 +C2) which is not the same thing.