: Astronomie: Riccati equation

mathematical technique > mathematical analysis > differential equation > Riccati equation

Riccati equation

In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form y′(x) = q₀(x) + q₁(x)y(x) + q₂(x)y²(x) where q₀(x) ≠ 0 and q₂(x) ≠ 0. If q₀(x) = 0 the equation reduces to a Bernoulli equation, while if q₂(x) = 0 the equation becomes a first order linear ordinary differential equation. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riccati_equation)

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