Differential Equations with Forcing: Method of Undetermined Coefficients @Eigensteve

Uploaded November 2022 | Updated September 2026, 2 weeks ago

This video introduces external forcing to linear differential equations, and we show how to solve these equations with the method of undetermined coefficients. The idea is simple: 1) solve the unforced, or "homogeneous" system; 2) find a particular solution that equals the forcing when plugged into the ODE (generally, we guess the form of the solution based on the form of the forcing); 3) combine the homogeneous and particular solutions and use this full solution to identify the unknown coefficients with initial conditions.

Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/

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This video was produced at the University of Washington

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0:00 Overview and problem setup
7:02 Step 1: Solve homogeneous differential equation
8:45 Step 2: Solve for the particular solution
13:50 Step 3: Solve for coefficients with initial conditions

Differential Equations with Forcing: Method of Undetermined Coefficients

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