# 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.

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

Chapter 3 Topics

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