伯努利微分方程是形式如 的常微分方程。

代入 （注意 ）：

此一阶常微分方程可用积分因子求解。

In mathematics, an ordinary differential equation of the form

is called a Bernoulli equation when n≠1, 0. It is named after Jacob Bernoulli who discussed it in 1695. Bernoulli equations are special because they are nonlinear differential equations with known exact solutions. A famous special case of the Bernoulli differential equation is the logistic differential equation.