DIFFERENTIAL EQUATIONS explained in 21 Minutes

This video aims to provide what I think are the most important details that are usually discussed in an elementary ordinary differential equations (ODE) course, in just about 21 minutes. Simple examples are also provided (I, as an applied physics major, yearn for examples.). This video is divided into five chapters. CHAPTER 1: INTRODUCTION 0:00 1.1: Definition 0:30 1.2: Ordinary vs. Partial Differential Equations 1:24 1.3: Solutions to ODEs 2:49 1.4: Applications and Examples CHAPTER 2: FIRST ORDER DIFFERENTIAL EQUATIONS 3:14 2.1: Separable Differential Equations 4:10 2.2: Exact Differential Equations 6:01 2.3: Linear Differential Equations and the Integrating Factor CHAPTER 3: HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS 7:57 3.1: Theory of Higher Order Differential Equations 10:43 3.2: Homogeneous Equations with Constant Coefficients 13:04 3.3: Method of Undetermined Coefficients 14:44 3.4: Variation of Parameters CHAPTER 4: LAPLACE TRANSFORM 16:18 4.1: Laplace and Inverse Laplace Transforms 17:41 4.2: Solving Differential Equations using Laplace Transform CHAPTER 5: SUMMARY 19:15 5.1: Overview of Advanced Topics 20:28 5.2: Conclusion This video is designed to be beginner-friendly and focuses on finding analytical solutions to ODEs, since ngl these are the topics that my ODE class covered and the ones that I can explain confidently. 3Blue1Brown's video on ODEs offers a more intuitive and geometric approach to the topic. This video is animated using Manim, a Python math animation engine developed by 3Blue1Brown. Voice-overs are provided by me. Feel free to suggest improvements, and point out the possible mistakes I have made in this video. I hope this video is helpful for understanding at least the basic concepts in ODEs. Please subscribe and support this small channel for more uploads!