Chapter 1 - First-Order Differential Equations - 1.6 First-Order Linear Differential Equations - True-False Review - Page 59: a

False

For for a differential equation of the form $y′ + p(x)y = q(x)$, there exist an integrating factor $r(x)$. The same for $cr(x)$ where $c \ne 0$ is both constant and integrating factor. We can see that the integrating factor is independent of $q(x)$. Since we can choose any constant we want, there is not a unique solution to the integrating factor.