Definition:Bernoulli's Equation

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 Bernoulli's equation as a Bernoulli equation.

Also see

• Solution to Bernoulli's Equation for its general solution:

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

Source of Name

This entry was named for Jacob Bernoulli.

Historical Note

Bernoulli's equation was first solved by Jacob Bernoulli and Johann Bernoulli, and also Gottfried Wilhelm von Leibniz.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 18$: Basic Differential Equations and Solutions: $18.3$: Bernoulli's equation
• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.10$: Problem $3$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Bernoulli equation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Bernoulli's equation: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Bernoulli's equation: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Bernoulli equation