Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair

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While we saw a specific example of Constant Coefficient Homogeneous ODEs in my previous video in the playlist, in this video we're going to solve it in generality and really elaborate on the three main cases. The characteristic equation aka auxiliary equation can have either real and distinct root, real and repeated roots, or complex conjugates. Each of these three cases has a specific form of the solution to the differential equation.

0:00 Characteristic Equation
1:50 Three Cases
4:00 Real Distinct Roots
4:24 Real Repeated Roots
6:19 Complex Roots
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Видео Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair канала Dr. Trefor Bazett