flame_ode, a Python code which 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:

python_ode, Python codes which sets up various systems of 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:

ripple_euler used euler() to solve the problem.

Last revised on 09 November 2020.