1. The problem statement, all variables and given/known data Consider the general linear homogeneous second order equation: P(x)y'' + Q(x)y' + R(x)y = 0 (1) We seek an integrating factor μ(x) such that, upon multiplying Eq. (1) by μ(x), we can write the resulting equation in the form [μ(x)P(x)y']' + μ(x)R(x)y = 0 (2) (a) By equating coefficients of y' in Eqs. (1) and (2), show that μ must be a solution of: Pμ' = (Q - P')μ (3) 2. Relevant equations I guess the only relevant equation is the product rule of differentiation: [a(x)b(x)]' = a'(x)b(x) + a(x)b'(x) 3. The attempt at a solution Here is what I have done so far: By setting (1) = (2) P(x)y'' + Q(x)y' + R(x)y = [μ(x)P(x)y']' + μ(x)R(x)y Py'' + Qy' + Ry = μPy'' + μP'y' + μ'Py' + μRy Py'' + Qy' + Ry = μPy'' + (μP' + μ'P)y' + μRy Equating coefficients of y': Q = μP' + μ'P So: Pμ' = Q - P'μ, which is not the form that the book stated, Pμ' = (Q - P')μ So am I missing something in the derivation, or is it that the book's statement is wrong? By the way, this is Problem 11 in Section 11.1 of the book called Elementary Differential Equations and Boundary Value Problems by Boyce & DiPrima (9th Edition). Part (b) of the problem is just solving the differential equation to find μ(x), and I'm pretty sure that I can do that part. Anyway, I would really appreciate any input.