Definition:Bernoulli's Equation

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Definition

Bernoulli's equation is a first order ordinary differential equation which can be put into the form:

$\dfrac {\d y} {\d x} + \map P x y = \map Q x y^n$

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


Also known as

Some sources report this as a Bernoulli equation.


Also see

Solution to Bernoulli's Equation for its general solution:

$\displaystyle \dfrac {\map \mu x} {y^{n - 1} } = \paren {1 - n} \int \map Q x \, \map \mu x \rd x + C$

where:

$\map \mu x = e^{\paren {1 - n} \int \map P x \rd x}$


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


  • Results about Bernoulli's equation can be found here.


Source of Name

This entry was named for Jacob Bernoulli.


Sources