Linear Second-Order Differential Equations Part 1: Homogeneous Case

After a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these, let's first examine the simplest case, a linear homogenous second-order differential equation that exhibits constant coefficients. To solve these we will need to find a characteristic equation and do some algebra, a process which will vary depending on whether we are dealing with real distinct roots, complex roots, or a repeated root. Let's take a look!Script by Lorcan NichollsWatch the whole Differential Equations playlist: http://bit.ly/ProfDaveDiffeqWatch the whole Mathematics playlist: http://bit.ly/ProfDaveMathClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2General Chemistry Tutorials: http://bit.ly/ProfDaveGenChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices