Question

integrating factor for linear differential equations

Answer 1

... What?

Answer 2

it is a factor which when multiplied both sides to a linear ODE becomes an exact differential

Answer 3

\[y'+p(x)y=q(x)\\\qquad\qquad\mu(x)=e^{\int p(x)\mathrm dx}\\\big(\mu (x)y(x)\big)'= \mu (x)q(x)\]