In mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form
where is a real number. Some authors allow any real ,[1][2] whereas others require that not be 0 or 1.[3][4] The equation was first discussed in a work of 1695 by Jacob Bernoulli, after whom it is named. The earliest solution, however, was offered by Gottfried Leibniz, who published his result in the same year and whose method is the one still used today.[5]
Bernoulli equations are special because they are nonlinear differential equations with known exact solutions. A notable special case of the Bernoulli equation is the logistic differential equation.
^Cite error: The named reference Zill 10E was invoked but never defined (see the help page).
^Cite error: The named reference Stewart Calculus was invoked but never defined (see the help page).
^Cite error: The named reference EOM was invoked but never defined (see the help page).
^Cite error: The named reference Teschl was invoked but never defined (see the help page).
^Parker, Adam E. (2013). "Who Solved the Bernoulli Differential Equation and How Did They Do It?" (PDF). The College Mathematics Journal. 44 (2): 89–97. ISSN 2159-8118 – via Mathematical Association of America.
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