flame_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) whose solutions start as ripples and end as hyperbolas.


The computer code and data files described and made available on this web page are distributed under the MIT license


ripple_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:


matlab_ode, MATLAB codes which set up various ordinary differential equations (ODE).


  1. John D Cook,
    Ripples and Hyperbolas,
    Posted 06 November 2020.
  2. Wendell Mills, Boris Weisfeiler, Allan Krall,
    Discovering Theorems with a Computer: The Case of y‘ = sin(xy),
    The American Mathematical Monthly,
    Volume 86, Number 9, November 1979, pages 733-739.

Source Code:

Last revised on 07 November 2020.