# Bernoulli Equation

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## Bernoulli equation

[ber‚nü·lē i′kwā·zhən] (fluid mechanics)

(mathematics)

A nonlinear first-order differential equation of the form (

*dy*/*dx*) +*yf*(*x*) =*y*(^{n}g*x*), where*n*is a number different from unity and*f*and*g*are given functions. Also known as Bernoulli differential equation.## Bernoulli Equation

a differential equation of the first order of the form

*dy*/*dx* + *Py* = *Qy*^{α}

where *P* and *Q* are predetermined continuous functions of *x* and α is a constant. With the introduction of the new function z = y^{-α} + ^{1}, the Bernoulli equation is reduced to a linear differential equation with respect to *z.* The Bernoulli equation was considered by Jakob Bernoulli in 1695, and a method of solving it was published by Johann Bernoulli in 1697.