Definition:Bernoulli's Equation

Definition
Bernoulli's equation is a first order ordinary differential equation which can be put into the form:
 * $\dfrac {\mathrm d y}{\mathrm d x} + P \left({x}\right) y = Q \left({x}\right) y^n$

where $n \ne 0$ and $n \ne 1$.

Also see
Solution to Bernoulli's Equation for its general solution:
 * $\displaystyle \frac {\mu \left({x}\right)} {y^{n - 1} } = \left({1 - n}\right) \int Q \left({x}\right) \mu \left({x}\right) \, \mathrm d x + C$

where:
 * $\mu \left({x}\right) = e^{\left({1 - n}\right) \int P \left({x}\right) \, \mathrm d x}$

When $n = 0$ or $n = 1$ the equation is linear, and Solution to Linear First Order Ordinary Differential Equation can be used.