411 REFERENCE · Wikibooks
Ordinary Differential Equations/d'Alembert
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
The d'Alembert's Equation, which is sometimes called the Lagrange equation was solved by John Bernoulli before 1694, and d'Alembert studied its singular solutions in a 1748 publication. It is essentially an equation of the form
Where and are functions of .
Take the derivative
Now write this equation as
Then it is a linear equation with dependent variable x and independent variable .