Chapter 2.3, Problem 55E

In determining the integrating factor (3), we did not use a constant of integration in the evaluation of ∫P(x) dx. Explain why using ∫P(x) dx + c₁ has no effect on the solution of (2).

μ(x) = e^∫p(x)dx    (3)

$\frac{dy}{dx}+P\left(x\right)y=f\left(x\right)$.        (2)