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Briot-Bouquet Equation

An ordinary differential equation of the form

x^my^'=f(x,y),

where m is a positive integer, f is analytic at x=y=0, f(0,0)=0, and f_y^'(0,0)!=0.

Zwillinger (1997, p. 120), citing Ince (1956, p. 295), define the Briot-Bouquet equation as

xy^'-lambday=a_(10)x+a_(20)x^2+a_(11)yx+a_(02)y^2+....

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References

Briot, C. and Bouquet, J. "Propriétés des fonctions définie par des équations différentielles." J. l'Ecole Polytechnique, Cah. 36, 133-198, 1856.Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, pp. 481-482, 1988.Ince, E. L. Ordinary Differential Equations. New York: Dover, 1956.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 120, 1997.

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Briot-Bouquet Equation

Cite this as:

Weisstein, Eric W. "Briot-Bouquet Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Briot-BouquetEquation.html

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