Khan Academy Differential Equations
Unknown
Khan Academy unit of short videos on linear second-order differential equations, covering the characteristic equation with real, complex, and repeated roots, and the method of undetermined coefficients. Learners can solve homogeneous and nonhomogeneous constant-coefficient equations.
More resources on Second-Order ODEs
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Introduction to Differential Equations
Learn differential equations: explore methods for solving, modeling, and analyzing them. Taught by the Khan Academy Team.
MIT Mathlets
Browser-based applets from MIT's 18.03 course. Damped Vibrations, Amplitude and Phase: Second Order, Forced Damped Vibration, and Harmonic Frequency Response let you move characteristic roots, damping, and driving frequency and watch solutions respond.
Notes on Diffy Qs: Differential Equations for Engineers
Free open textbook by an Oklahoma State mathematician. Chapter 2 treats higher-order linear ODEs: constant-coefficient solutions, undetermined coefficients, variation of parameters, mechanical vibrations, and forced oscillations with resonance, each with exercises, solutions, and Sage animations.
Differential Equations for Engineers
This course is all about differential equations and covers both theory and applications. In the first five weeks, students will learn about ordinary differential equations, while the sixth week is an introduction to partial differential equations. The course includes 56 concise lecture videos, with a few problems to solve after each lecture. After each major topic, there is a short practice quiz. At the end of each week, there is an assessed quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/differential-equations-for-engineers.pdf Watch the promotional video from the link https://youtu.be/eSty7oo09ZI