Question

When do you use an integrating factor when solving ODEs?

Answer 1

When solving ODEs, I usually get x's on one side y's on the other and integrate. However, in some questions I heard that I needed to use an integrating factor to solve the ODE.

Just wondering how I can I tell if need use integrating factor?

Answer 2

When DE is of the form,
\[\mathsf{\frac{dy}{dx} + P(x)y = Q(x)}, \quad \mathsf{\text{where P(x) and Q(x) are functions of x only or constants.}}\]