**Definition** A *Bernoulli equation* is a first order [[Ordinary Differential Equation|ODE]] of the form $\frac{d}{dt} x(t) = - p(t)x(t) + q(t) x^{n}(t), \quad t \in (\alpha,\beta) \subset \mathbb{R},$with $n \in \{2,3,4,\dots\}$ and $p,q$ given functions. # Properties See [[Solution to Bernoulli Equation]]. Bernoulli equations are special because they are [[Linear Differential Equation|non-linear ODE]] with known exact solutions. A notable special case of the Bernoulli equation is the [[Logistic Differential Equation]].