When can you use Series to solve ODEs? Ordinary vs Singular Points

Series solutions can often be extremely powerful for solving differential equations, particular linear homogeneous ones whose coefficients are nice, what we will describe as being analytic in this video. But when, exactly, do these apply? In this video we will dive a bit into the theory of series solutions to solve ODEs. We are going to see that there are two types of points, ordinary points and singular points. For ordinary points we get a nice theorem that says not only do we have a convergent power series solutions, but also it tells us the radius of convergence is at least as large as the distance to he nearest singular point on the complex plane. For the first video on Series Solutions in the ODE playlist click here:    • How to solve ODEs with infinite series | I...   **************************************************** 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