> [!definition] > > Let $(L)$ be a first order [[Ordinary Differential Equation|ODE]]. $(L)$ is **separable** if > $ > y^\prime = f(t, y) = P(t)Q(y) > $ > where $P$ depends on $t$ only and $Q$ depends on $y$ only. > > $ > \frac{dy}{dt} = PQ \Rightarrow \int\frac{1}{Q}dy = \int P dt > $ > > Which can be solved by rearranging the terms.