Differential Equations Final Exam Study Guide and Equation Sheet

Hey everyone! I’m totallyintomath, and this is the equation sheet I handwritten in the Spring 2019 semester to use while taking my Differential Equations final exam. Unlike most equations sheets, this one serves as a helping hand, giving you not only the necessary equations you’ll need for the exam, but also tips about how to answer certain types of questions. These equations even have explanations of each component involved (because sometimes symbols alone can be confusing) and when to use the equation. Each sentence or diagram is a guide to prevent simple mistakes and common misconceptions. There are fourteen total sections, one for each chapter covered in the course. All the equations and important information are organized by chapter (and within a specific concept) so that navigating through these four pages can be easy and stress-free. The topics covered in this study-guide include the following: How to Verify a Solution Explicit v. Implicit How to Know if a Differential Equation (DE) is nonlinear Existence and Uniqueness Theorem Boundary-Value Problem (BVP) and Interval of Definition Normal or General Form of a DE How to Construct Phase Portraits How to Solve Separable DE How to Solve Linear DE How to Solve Exact DE Making an Non-exact DE into an Exact DE Linear Models (including Radioactive Decay and Newton’s Law of Cooling) Logistic Equation (including the modified version with h) Existence and Uniqueness Theorem for Linear DE Reduction of Order How to Solve Homogeneous Linear DE with Constant Coefficients The Superposition Method The Variation of Parameters Method How to Solve Cauchy-Euler DE This document is perfect for students who don’t have the time to make their own, can’t find an exceptional one online, or have no idea where to start studying. To make the most effective use out of this study guide, I would recommend highlighting the most important parts to really hammer in what has to be understood. Though this was created while I was at Tunxis Community College, anyone from any school can benefit by reviewing this equation sheet. About the author: I’m totallyintomath, a young, motivated college freshman (as of 2019) majoring in Mathematics. Though I’m not entirely sure where mathematics will lead me, all I know is that I take great pride and passion in my hard work and wish to pursue this field further. One day, I decided that I could achieve even greater ambitions, fought immensely to earn ten high school credits in one year, and graduated a year early. Unfortunately, I could only attend community college because I didn’t have an SAT score. That was where my college journey began, leaving my high school behind to find something even better than myself.