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Ordinary Differential Equations/d'Alembert

< Ordinary Differential Equations

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 f and g are functions of y'.

Take the derivative


Now write this equation as

Then it is a linear equation with dependent variable x and independent variable y'.