6.20 General method continued

The equation $\frac{dy}{dx}+p(x)y=q(x)$ therefore becomes:

after multiplying. This is an integrable equation, and can therefore be solved by integrating.

This is exactly what we did in the example on slide 6.16, where the integrating factor is $e^{x^{2}}$.

What about the constant? Strictly speaking, we should recall that $\int p(x)\,dx$ is only defined up to addition of a constant $c$. In the notation of slide 6.18, we should be able to replace the function $F(x)$ by $F(x)+c$. Question: why does $c$ not matter here?