How to Solve Constant Coefficient Homogeneous Differential Equations скачать в хорошем качестве

How to Solve Constant Coefficient Homogeneous Differential Equations

MY DIFFERENTIAL EQUATIONS PLAYLIST: ►   • Ordinary Differential Equations (ODEs)   Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs One class of second order ODEs is particularly nice: constant coefficient homogeneous ones. That is, it is linear in the dependent variable and its coefficients, and the right hand side is just zero. For this class, we make a guess or ansatz that the solution is an exponential. Plug that it and you get something called the characteristic equation or the auxiliary equation. Solve that via the quadratic formula and the roots tell you the types of exponentials. It turns out that there are really three cases that can arise, and I'll break those three cases down in the next video. For now we do a full initial value problem (IVP) from start to finish to introduce the methodology ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON:   / drtrefor   ►MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett ►CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ►CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV):    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ►Cool Math Series:    • Cool Math Series   ►Learning Math Series:    • 5 Tips To Make Math Practice Problems Actu...   ►LaTeX:    • Intro to LaTeX **Full Tutorial**  Part II ...   SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok:   / drtrefor   ►Instagram (photography based):   / treforphotography