Briot-Bouquet Equation

An ordinary differential equation of the form

where  is a positive integer,  is analytic at , , and 

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

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.