d'Alembert's equation

Template:Short description

Script error: No such module "Distinguish". Script error: No such module "Unsubst". In mathematics, d'Alembert's equation, sometimes also known as Lagrange's equation,^[1] is a first order nonlinear ordinary differential equation, named after the French mathematician Jean le Rond d'Alembert. The equation reads as^[2]

y = x f (\frac{d y}{d x}) + g (\frac{d y}{d x}) .

After differentiating once, and rearranging with $p = d y / d x$ , we have

\frac{d x}{d p} + \frac{x f^{'} (p) + g^{'} (p)}{f (p) - p} = 0

The above equation is linear. When $f (p) = p$ , d'Alembert's equation is reduced to Clairaut's equation.

References

↑ Script error: No such module "citation/CS1".
↑ Davis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962.

Script error: No such module "Check for unknown parameters".

Template:Math-physics-stub Template:Asbox

[1] Script error: No such module "citation/CS1".

[2] Davis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962.

[1]

[2]

d'Alembert's equation

References

Navigation menu

Search