Maxima by Example, Ch. 3: Ordinary Differential Equation Tools

Ted Woollett

The Dec. 2017 update changes a crucial typo relating to Ex. 4 (Linear Oscillator with Damping) and Ex. 5 (Underdamped Linear Oscillator with Sinusoidal Driving Force). The syntax of the Maxima function ic2 should look like:
ic2 (----,'diff(x,th) = 0), for example, and the crucial apostrophe was missing in the original posted examples.

This chapter has many examples of the use of plot2d. Before you read and try out the examples, run the appropriate plot2dtest file available above the Ch. 1 section. You may need to use one of the draw2d substitutes, depending on the version of Maxima you are using.

  1. --mbe3ode1.pdf : Dec. 21, 2017, Maxima 5.18.1, 44 pages
  2. --mbe3ode1.tex : Dec. 21, 2017, Latex code file
  3. --mbe3toc.txt : Detailed Table of Contents, July, 19, 2009
  4. --mbe3code.txt : Code input text file: Dec. 21, 2017, Maxima 5.18.1

Chapter 3 Topics

  1. Solution of One First Order Ordinary Differential Equation (ODE)
  2. Exact Solution with ode2 and ic1
  3. Exact Solution with desolve
  4. Numerical Solution and Plot with plotdf
  5. Numerical Solution with Fourth Order Runge-Kutta: rk
  6. Solution of One Second Order or Two First Order ODE's
  7. Exact Solution with ode2, ic2, and eliminate
  8. Exact Solution with desolve, atvalue, and eliminate
  9. Numerical Solution and Plot with plotdf
  10. Numerical Solution with Fourth Order Runge-Kutta: rk
  11. Ex.1: Fall in Gravity with Air Friction: Terminal Velocity
  12. Ex.2: One Nonlinear First Order ODE
  13. Ex.3: One First Order ODE Which is Not Linear in Y'
  14. Ex.4: Linear Oscillator with Damping
  15. Ex.5: Underdamped Linear Oscillator with Sinusoidal Driving Force
  16. Ex.6: Regular and Chaotic Motion of a Driven Damped Planar Pendulum
  17. Using contrib_ode for ODE's