The ordinary differential equation
 |
where 
and 
and 
are given functions. This equation is sometimes also known as Lagrange's
equation (Zwillinger 1997).
d'Alembert's Equation
See also
Lagrange's EquationExplore with Wolfram|Alpha
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.Cite this as:
Weisstein, Eric W. "d'Alembert's Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/dAlembertsEquation.html