• In mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form y ′ + P ( x ) y = Q ( x ) y n , {\displaystyle...
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  • Bernoulli equation may refer to: Bernoulli differential equation Bernoulli's equation, in fluid dynamics Euler–Bernoulli beam equation, in solid mechanics...
    192 bytes (52 words) - 20:50, 27 December 2019
  • Thumbnail for Jacob Bernoulli
    with its integration meaning. In 1696, Bernoulli solved the equation, now called the Bernoulli differential equation, y ′ = p ( x ) y + q ( x ) y n . {\displaystyle...
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  • potential theory Bernoulli differential equation Cauchy–Euler equation Riccati equation Hill differential equation Gauss–Codazzi equations Chandrasekhar's...
    13 KB (1,097 words) - 15:29, 28 May 2025
  • "Bernoulli Differential Equation". mathworld.wolfram.com. Retrieved 2024-06-02. Hille, Einar (1894). Lectures on ordinary differential equations. Addison-Wesley...
    39 KB (2,094 words) - 05:37, 24 June 2025
  • non-uniqueness of solutions. Jacob Bernoulli proposed the Bernoulli differential equation in 1695. This is an ordinary differential equation of the form y ′ + P (...
    29 KB (3,631 words) - 15:23, 23 April 2025
  • Thumbnail for Logistic function
    less than 1, it grows to 1. The logistic equation is a special case of the Bernoulli differential equation and has the following solution: f ( x ) =...
    56 KB (8,069 words) - 19:52, 23 June 2025
  • A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...
    36 KB (5,634 words) - 11:32, 24 June 2025
  • 2024. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli trial Bernoulli's principle...
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  • the element to bend. Bernoulli differential equation Bernoulli's equation Bernoulli's principle In fluid dynamics, Bernoulli's principle states that...
    67 KB (6,467 words) - 06:55, 24 April 2025
  • In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function...
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  • Thumbnail for Euler–Bernoulli beam theory
    were the first to put together a useful theory circa 1750. The Euler–Bernoulli equation describes the relationship between the beam's deflection and the applied...
    47 KB (7,388 words) - 16:52, 4 April 2025
  • architect Bernoulli differential equation Bernoulli distribution and Bernoulli random variable Bernoulli's inequality Bernoulli's triangle Bernoulli number...
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  • Thumbnail for Ordinary differential equation
    In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other...
    44 KB (5,187 words) - 16:53, 2 June 2025
  • Thumbnail for Partial differential equation
    In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...
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  • Bernoulli family of Basel. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli Society...
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  • Johann Bernoulli in the eighteenth century) of finding an analogy between the propagation of light and the motion of a particle. The wave equation followed...
    44 KB (8,210 words) - 22:52, 28 May 2025
  • A famous special case of the Bernoulli equation is the logistic differential equation. Bernoulli's equation An equation for relating several measurements...
    279 KB (31,761 words) - 16:43, 17 July 2025
  • Young–Laplace–Gauss equation, as Carl Friedrich Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions...
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  • In mathematics, a differential equation is called Darboux differential equation if it satisfies the form M ( x , y ) d x − L ( x , y ) d y + N ( x , y...
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  • homogeneous equation obtained by removing the constant term. The term homogeneous was first applied to differential equations by Johann Bernoulli in section...
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  • mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in...
    20 KB (5,225 words) - 07:01, 9 November 2024
  • In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written...
    30 KB (4,754 words) - 18:32, 3 July 2025
  • Thumbnail for Physics-informed neural networks
    Physics-informed neural networks (category Differential equations)
    data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering...
    38 KB (4,835 words) - 08:26, 11 July 2025
  • Euler–Bernoulli beam equation with time-dependent loading Airy equation Schrödinger equation Klein–Gordon equation nonlinear Schrödinger equation Korteweg–de...
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  • Jakob Bernoulli's honour: Bernoulli's formula Bernoulli differential equation Bernoulli's inequality Bernoulli numbers Bernoulli polynomials Bernoulli's quadrisection...
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  • Thumbnail for Bessel function
    systematically study them in 1824, are canonical solutions y(x) of Bessel's differential equation x 2 d 2 y d x 2 + x d y d x + ( x 2 − α 2 ) y = 0 {\displaystyle...
    76 KB (12,308 words) - 06:31, 12 June 2025
  • In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form y ( x ) = x d y d x + f ( d y d x ) {\displaystyle...
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  • A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when...
    32 KB (4,835 words) - 15:41, 24 April 2025
  • integral in calculus Lemniscate of Bernoulli Solution of differential equation by separation of variables Nicolaus I Bernoulli's s contributions: Orthogonal...
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