Jacobi equation
From Encyclopedia of Mathematics
A first-order ordinary differential equation
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or, in a more symmetric form,
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where all the coefficients are constant numbers. This equation, which is a special case of the Darboux equation, was first studied by C.G.J. Jacobi [1]. The Jacobi equation is always integrable in closed form by using the following algorithm. First one finds by direct substitution at least one particular linear solution
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Then one makes the changes of variables
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to obtain an equation that is reducible to a homogeneous equation.
References
[1] | C.G.J. Jacobi, "De integratione aequationis differentialis ![]() |
[2] | W.W. [V.V. Stepanov] Stepanow, "Lehrbuch der Differentialgleichungen" , Deutsch. Verlag Wissenschaft. (1956) (Translated from Russian) |
[3] | E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1947) |
Comments
References
[a1] | E.L. Ince, "Ordinary differential equations" , Dover, reprint (1956) |
How to Cite This Entry:
Jacobi equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jacobi_equation&oldid=40763
Jacobi equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jacobi_equation&oldid=40763
This article was adapted from an original article by N.Kh. Rozov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article