y'' + 2y' + y = e^(-t)

Determine the particular solution to the given differential equation y'' + 2y' + y = e^-t. In other words, find the particular solution to the given non-homogenous differential equation y'' + 2y' + y = 1/e^t using variation of parameters with characteristic/auxiliary equations and roots.

Link to Differential Equations playlist:    • Differential Equations  

Hey everyone, I hope you learned and understood the Differential Equations problem (Solving Non-Homogenous Differential Equations with Variation of Parameters) a little better. Feel free to ask me any questions or give me suggestions in the comments below. If you enjoyed the video, please give it a thumbs up. Thanks!

Separable Equations, Integration examples, integral examples, antiderivative examples, differential equations, integral practice problems, calculus 1 practice problems, differential equations practice problems, initial value problem, approximate solution, characteristic equations, auxiliary equations, roots, root solutions, complex roots, method of undetermined coefficients, variation of parameters. James Stewart Single Variable Calculus. Nagle, Saff, Snider Fundamentals of Differential Equations. In Problems 1-8, find a general solution to the differential equation the method of variation of parameters. y'' + 2y' + y = e^-t.

This video is part of a comprehensive walkthrough of the most common problems you will run into during Differential Equations. I hope you find this playlist helpful!