Using Laplace Transforms to solve Differential Equations ***full example***

How can we use the Laplace Transform to solve an Initial Value Problem (IVP) consisting of an ODE together with initial conditions? in this video we do a full walkthrough beginning with the differential equation, converting it to an algebraic equation via the Laplace Transform, solving that algebraic equation, and finally converting back to a solution to the IVP through the Inverse Laplace Transform. This is part of my series on the Laplace Transforms in my Differential Equations Playlist: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON: https://patreon.com/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: 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 ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw ►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho ►Learning Math Series: https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►LaTeX: https://www.youtube.com/watch?v=-HvRvBjBAvg&list=PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73&index=2&ab_channel=Dr.TreforBazett SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok: http://tiktok.com/@drtrefor ►Instagram (photography based): http://instagram.com/treforphotography