Mathematics (All Of It) - 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 Nicholls Watch the whole Differential Equations playlist: http://bit.ly/ProfDaveDiffeq Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1 Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2 General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem Biology Tutorials: http://bit.ly/ProfDaveBio EMAIL► [email protected] PATREON► http://patreon.com/ProfessorDaveExplains Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience! Amazon: https://amzn.to/2HtNpVH Bookshop: https://bit.ly/39cKADM Barnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT