The Theory of Higher Order Differential Equations

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Previously in my ODE Playlist we've talked about the theory of 1st order or 2nd order differential equations. Now we turn to the more general nth order ODE, specifically focusing on linear homogeneous ODEs. A lot of the theory is the same, but we have a few complications to deal with. Firstly, we have a new Existence and Uniqueness theorem for linear ODEs. Next, we have the principle of superposition which allows us to take linear combinations of solutions and deduce new solutions. Finally we describe the method to find the general solution to an nth order ODE and use the Wronskian to verify linear independence of the fundamental set of solutions:

0:00 Linear nth order ODEs
1:52 Existence & Uniqueness
3:20 Superposition
5:00 General Solution
7:02 The Method

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Видео The Theory of Higher Order Differential Equations канала Dr. Trefor Bazett