Worked Examples
This page is a compendium of fully worked examples for MATH 341 Differential Equations during the Fall 2026 semester. Sections may be added or edited as the course progresses. The examples linked here are not meant to substitute for those in the course textbook (Logan 2015). They are also not meant to be a substitute for attending lectures.
Showing a function is a solution works through the details of showing that a particular function solves a particular differential equation.
First-order equations worked examples for first-order equations including topics such as sketching slope-fields, finding general solutions and solutions to initial value problems for separable and linear equations, integrating factors, and applications to mechanics, population biology, and electric circuits.
Second-order linear constant coefficient equations provides worked examples for second-order linear equations with constant coefficients including topics such as homogeneous equations, nonhomogeneous equations and undetermined coefficients. Initial value problems and applications are also considered.
Variation of parameters provides worked examples solving second-order linear equations with non-constant coefficients using the method of variation of parameters. Initial value problems and applications are also considered.
Laplace transforms provides worked examples computing Laplace transforms and inverse transforms.
More on Laplace transforms provides worked examples related to using Laplace transforms to solve ODEs, the convolution property, and impulse forces.
Matrices and linear algebra provides worked examples related to using matrices and linear algebra including eigenvalues.
Solving linear systems provides worked examples related to solving linear systems.
Phase plane analysis & nonhomogeneous systems provides worked examples related to phase plane analysis of linear systems and nonhomogeneous systems.
Nonlinear systems provides worked examples related to phase plane analysis of nonlinear systems.
Numerical solutions provides worked examples for numerical solutions of ODEs.
Access Jupyter Notebooks
Each section of examples has an associated Jupyter notebook, which can be run via Google Colab. Just click the “Open in Colab” button below for the notebook you want. The notebooks contain all of the code used in the examples, and can be modified for exploring on your own.
| Notebook | Open in Colab |
|---|---|
| Examples 1 |  |
| Examples 2 | |
| Examples 3 | |
| Examples 4 | |
| Examples 5 | |
| Examples 6 | |
| Examples 7 | |
| Examples 8 | |
| Examples 9 | |
| Examples 10 | |
| Examples 11 | |