How to solve ODEs with infinite series | Intro & Easiest Example: y'=y

In this video we see how to find series solutions to solve ordinary differential equations. This is an incredibly powerful tool that really expands the amount of differential equations we can solve. We will first introduce power series and their basic principles, along with the standard series expandions for sin(x), cos(x), e^x and 1/(1-x), the geometric series. We'll then see how to substitute the series solution into the differential equation, manipulate indices, and get a recurrence relation on the coefficients. By studying this recurrence relation we can recover the familiar answer to y'=y that has a solution of e^x. This video is part of a Differential Equations playlist, so go there to check out the next video on series solutions which dives a bit more into the theory behind this. ODE playlist:    • Laplace Transforms and Solving ODEs   **************************************************** Other Course Playlists: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS III:    • Calculus III: Multivariable Calculus (Vect...   ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series:    • 5 Tips To Make Math Practice Problems Actu...   ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   **************************************************** ►Follow me on Twitter:   / treforbazett   ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett