Chapter 6.5, Problem 39E

Using an Integrating Factor The expression $u(x)$ is an integrating factor for $y^{\prime }+P(x)y=Q(x)$. Which of the following is equal to $u^{\prime }(x)$? Verify your answer.

(a) $P(x)u(x)$

(b) $P^{\prime }(x)u(x)$

(c) $Q(x)u(x)$

(d) $Q^{\prime }(x)u(x)$