Condition for exact recognition that a linear DE is already in derivative form for JEE

Formula

\(\dfrac{dy}{dx}+p(x)y=q(x)\iff \dfrac{d}{dx}[\mu(x)y]=\mu(x)q(x)\) when \(\mu'(x)=p(x)\mu(x)\)

Variables: \(\mu(x)\) is the integrating factor.

Conditions: \(\mu(x)\neq 0\).

Transforming a linear DE into exact derivative form.