returns the Euler–Lagrange differential equation obeyed by u[x] derived from the functional f, where f depends on the function u[x] and its derivatives, as well as the independent variable x.
returns the Euler–Lagrange differential equation obeyed by u[x,y,…].
returns a list of Euler–Lagrange differential equations obeyed by u[x,y,…],v[x,y,…],….
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Basic Examples (2)
The solution to the pendulum equation can be expressed using the function JacobiAmplitude:
The brachistochrone problem asks for the curve of quickest descent. The time taken for a particle to fall an arc length is . If measures the decrease in height from an initial point of release, then the velocity satisfies: