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The Theory of 2nd Order ODEs // Existence & Uniqueness, Superposition, & Linear Independence

Dr. Trefor Bazett 75,761 lượt xem 4 years ago
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MY DIFFERENTIAL EQUATIONS PLAYLIST: ►https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs

Previously in our ODE playlist, we've studied 1st order differential equations. Now we move to second order differential equations, and specifically focus at the beginning on the major theory. What does existence and uniqueness look like for 2nd order linear ODEs? We see a remarkable property called superposition, and finally we get the big method which is to find two linearly independent solutions to the ODE which will form, by superposition, the the general solution

0:00 Linear ODEs
1:29 Existence 7 Uniqueness
3:38 Superposition
6:18 Linear Independence
7:32 General Solution

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