Product derivative after multiplying by integrating factor for JEE

Formula

\(\dfrac{d}{dx}\left[y\,e^{\int p(x)dx}\right]=q(x)e^{\int p(x)dx}\)

Variables: \(y\) is the dependent variable, \(p(x),q(x)\) are given functions.

Conditions: Equation must be in the form \(\dfrac{dy}{dx}+p(x)y=q(x)\).

Key transformation step in integrating factor method.