Hellow guys, Welcome to my website, and you are watching How to Solve Constant Coefficient Homogeneous Differential Equations. and this vIdeo is uploaded by Dr. Trefor Bazett at 2021-03-22T08:14:30-07:00. We are pramote this video only for entertainment and educational perpose only. So, I hop you like our website.
| Name | How to Solve Constant Coefficient Homogeneous Differential Equations |
| Video Uploader | Video From Dr. Trefor Bazett |
| Upload Date | This Video Uploaded At 22-03-2021 15:14:30 |
| Video Discription | MY DIFFERENTIAL EQUATIONS PLAYLIST: ►https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw 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 OTHER COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►LAPLACE TRANSFORM: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography |
| Category | Education |
| Tags | Solution | Example | math | ODE | Differential equation | constant coefficient | homogeneous | characteristic equation | auxiliary equation | roots | polynomial | real distinct | real repeated | complex roots | initial value problem | initial conditions | how to solve | second order | 2nd order |
