In applying the usual formula for y'+py=q with u=e(adsbygoogle = window.adsbygoogle || []).push({}); ^{∫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)*(x^{2}/2 +C). But if I were to put constants in for the integration factor, I get

exp(-x)*(C_{1}x^{2}+C_{2})

which is not the same thing.

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# Why no constant of integration for the integration factor?

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