Maple worksheets on second order differential equations |

Differential equations:

- First order differential equations
- Second order differential equations
- Partial differential equations and the 1-dimensional wave equation

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Homogeneous 2nd order linear differential equations with constant coefficients-homog2DE.mws

- Introductory example.
- General method of solution of homogeneous 2nd order linear DE's with constant coefficients.
- The case where the auxiliary equation has equal roots.
- The case where the auxiliary equation has complex roots.
- Summary of standard forms for the solution.

Non-homogeneous 2nd order linear differential equations with constant coefficients-undetcoeff.mws

- The general form of a second order linear differential equation.
- General method of solution of non-homogeneous 2nd order linear DE's with constant coefficients.
- Introduction to the method of undetermined coefficients for determining a particular solution.
- A table of standard trial particular solutions.

Non-homogeneous 2nd order linear differential equations: variation of parameters-varparam.mws

- Determining a particular integral by variation of parameters: theory.
- Variation of parameters: summary of method.
- Variation of parameters: examples.

A procedure for solving 2nd order linear differential equations with constant coefficients-desolveCC.mws

- A procedure for solving 2nd order linear DE's with constant coefficients:
desolveCC.- Examples

Simple harmonic motion and damped oscillations-oscillations.mws

- Simple harmonic motion
- Damped motion
- Over-damped systems
- Critically damped systems
- Under-damped systems

Forced oscillations-forced.mws

- Applying an external force to a damped system.
- The transient and steady state parts of a solution.
- Resonance .. introductory example.
- Beats .. introductory example.
- Resonance as a limiting situation with respect to the natural frequency and the frequency of the forcing term.
- An under-damped system for which the frequency of the forcing term coincides with the natural frequency.

Resonance of an under-damped oscillatory system-resonance.mws

- Genuine resonance and resonant angular frequency .. an example.
- Genuine resonance and resonant angular frequency .. general case.
- The dependence of the resonant angular frequency on damping.
- Summary.

A procedure for solving 2nd order differential equations with a "missing variable"-missingvar.mws

- A procedure for solving 2nd order DE's by substituting for the derivative:
desolveMV.- Examples with the dependent variable missing.
- Examples with the independent variable missing.

Procedures for differential equations- DEsol.zip