Differential Equations Examples

Math 243 - Fall 2025

Slope Fields

Figure: Slope field example (Octave, Python, Sage)

Euler’s Method

Figure: Euler’s method (Python)

Phase Planes

Figure: Example phase plane (Python, Octave)

Euler’s Method for Systems

Figure: Two-dimensional Euler’s method example (Python)

Finding Exact Eigenvectors and Eigenvalues

from sympy import *

A = Matrix([[3,5],[2,6]])
'''
The .eigenvects() method returns a list of tuples containing: 
1. an eigenvalue, 
2. its multiplicity (how many times it is a root), and
3. a list of corresponding eigenvectors. 
'''
pretty_print(A.eigenvects())

Figure: Finding exact eigenpairs. (Octave, Python)

Finding Solutions of Linear Homogeneous Systems

Figure: Solution curves for linear systems (Python)