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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.
The categorical distribution is the generalization of the Bernoulli distribution for variables with any constant number of discrete values. The Beta distribution is the conjugate prior of the Bernoulli distribution. [5] The geometric distribution models the number of independent and identical Bernoulli trials needed to get one success.
Bernoulli equation: 1 + = Class of differential equation which may be solved exactly [2] Binomial differential equation (′) = (,) Class of differential equation which may sometimes be solved exactly [3] Briot-Bouquet Equation: 1
These equations for solution of a first-order partial differential equation are identical to the Euler–Lagrange equations if we make the identification = ˙ ˙. We conclude that the function ψ {\displaystyle \psi } is the value of the minimizing integral A {\displaystyle A} as a function of the upper end point.
The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
An important application of the Riccati equation is to the 3rd order Schwarzian differential equation ():= (″ ′) ′ (″ ′) = which occurs in the theory of conformal mapping and univalent functions. In this case the ODEs are in the complex domain and differentiation is with respect to a complex variable.
Download as PDF; Printable version; In other projects ... move to sidebar hide. Bernoulli equation may refer to: Bernoulli differential equation; Bernoulli's equation ...
In May 1690, in a paper published in Acta Eruditorum, Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation. The isochrone, or curve of constant descent, is the curve along which a particle will descend under gravity from any point to the bottom in exactly the ...
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