The MathResource
Charpit's method,
n. a method for solving a first-order partial differential equation of the form

in which a solution of a specimen of Lagrange's linear equation is used to provide a second first-order partial differential equation

that has the property that solving these equations for ∂z/∂x and ∂z/∂y produces an integrable total differential equation

The general solution of this ordinary differential equation is a complete solution of the equation F = 0.