Bernoulli’s Equation


Posted in Math Formulas




Bernoulli’s Equation

An equation of the form \dfrac{dy}{dx} + Py = Qy^n \cdots \cdots (i) where P, Q are function of x above is called Bernoulli’s equation.

Note: To reduce it into linear

\dfrac{1}{y^n}.\dfrac{dy}{dx} + p.y^{-n + 1} = Q , \, put \, \, y^{-n + 1} \\ = v, \, \, then \, \, (-n + 1) y^{-n} \dfrac{dy}{dx} = \dfrac{dv}{dx}

So equation (i) reduces to \dfrac{dv}{dx} + (1- x)pv = (1- x)Q, which is linear in v.



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