Diff. Equations·Course
Differential Equations
Differential equations: first- and second-order ODEs, systems, PDEs, and applications in physics and engineering
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Solve first-order ODEs.
- 02Handle higher-order linear ODEs.
- 03Analyze systems of ODEs.
- 04Approach the main PDEs.
- 05Model real dynamics with differential equations.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Differential Equations [Online course]. Stoa. https://stoa.school/course/diff-equations
- MLA
Stoa. “Differential Equations.” Stoa, 2026, https://stoa.school/course/diff-equations.
- Chicago
Stoa. “Differential Equations.” Stoa. Accessed September 1, 2026. https://stoa.school/course/diff-equations.
§ 02 — Curriculum
6 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IFirst-Order ODEsSolution methods, singular solutions, geometric interpretation3 articles
18 minBegin → - M IIPicard’s TheoremExistence and uniqueness of solutions, continuation of solutions3 articles
18 minBegin → - M IIIHigher-Order Linear ODEsFundamental system of solutions, Wronskian, method of variation of parameters3 articles
18 minBegin → - M IVSystems of ODEsMatrix method, Wronskian, fundamental matrix3 articles
18 minBegin → - M VPhase Portrait and Critical PointsClassification of critical points, stability, limit cycles3 articles
18 minBegin → - M VILyapunov Stability TheoryLyapunov stability, Lyapunov functions, bifurcations3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Solve separable equations, linear first-order ODEs, and the Bernoulli equation
Solve linear ODEs with constant coefficients using the method of variation of parameters
Study systems of ODEs, phase portraits, and stability
Solve fundamental equations of mathematical physics by the method of separation of variables
§ 04 — Practices