Undetermined Coefficients Solving nonhomogeneous ODEs

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MY DIFFERENTIAL EQUATIONS PLAYLIST: ► • Ordinary Differential Equations (ODEs) • Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs • How can we solve an ordinary differential equation (ODE) like y''-2y'-3y=3e^2t. The problem is the non-homogeneity on the right hand side. If this was homogeneous and just zero, then previously in our playlist we've studied how to solve constant coefficient homogeneous equations. To deal with the non-homogeneity we use a method called undetermined coefficients. The big idea is to guess a so called particular solution with the same basic form as the right hand side, but with undetermined coefficients. Substitute everything in, and you can solve for the constants in your particular solution. Finally, the general solution is the sum of the homogeneous and the particular solution. I show all the standard guesses and how to deal with situations where there are repeats to the homogeneous in the particular. • 0:00 Non-homogeneous ODEs • 0:50 Particular vs Homogeneous Solutions • 4:00 Finding the Particular Solution • 6:45 Second Example • 9:15 Chart of standard guesses • 11:00 Third Example • BECOME A MEMBER: • ►Join: / @drtrefor • MATH BOOKS I LOVE (affilliate link): • ► https://www.amazon.com/shop/treforbazett • COURSE PLAYLISTS: • ►DISCRETE MATH: • Discrete Math (Full Course: Sets, Log... • ►LINEAR ALGEBRA: • Linear Algebra (Full Course) • ►CALCULUS I: • Calculus I (Limits, Derivative, Integ... • ► CALCULUS II: • Calculus II (Integration Methods, Ser... • ►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivariable Calculus ... • ►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Calculus (Line In... • ►DIFFERENTIAL EQUATIONS: • Ordinary Differential Equations (ODEs) • ►LAPLACE TRANSFORM: • Laplace Transforms and Solving ODEs • ►GAME THEORY: • Game Theory • OTHER PLAYLISTS: • ► Learning Math Series • • 5 Tips To Make Math Practice Problems... • ►Cool Math Series: • • Cool Math Series • SOCIALS: • ►X/Twitter: http://X.com/treforbazett • ►TikTok: / drtrefor • ►Instagram (photography based): / treforphotography

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