d'Alembert's Equation

The ordinary differential equation

where  and  and  are given functions. This equation is sometimes also known as Lagrange's equation(Zwillinger 1997).

REFERENCES:

Ince, E. L. Ordinary Differential Equations. New York: Dover, pp. 38-39, 1956.

Murphy, G. M. Ordinary Differential Equations and Their Solution. Princeton, NJ: Van Nostrand, pp. 65-66, 1960.

Valiron, G. The Geometric Theory of Ordinary Differential Equations and Algebraic Functions. Brookline, MA: Math. Sci. Press, pp. 217-218, 1950.

Zwillinger, D. "Lagrange's Equation." §II.A.69 in Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 120 and 265-268, 1997.