WEBVTT
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Okay, so we have the following system of different
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equations. So we have three. Why? Double
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prime plus find X and then minus two. Why
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is equal to zero? Sorry. Three x three
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extra crime. Those five X minus two by equal
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zero. And then we also have four. Why
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? Double prime Plus two. I minus six x
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is equal to zero. So this is to second
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order differential equations. And we would like to convert
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this system into a system of four first order differential
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questions. And the way we do this is is
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similar to what we've done before. We just start
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assigning names to all of our variables and their derivatives
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. But first, let's write down. Actually,
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the initial conditions we have is, well, we
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have x zero is equal to you. Negative one
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. Yeah. Ex prime of zero equals zero.
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Why? Zero is equal to one. And why
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prime of zero is equal to two. Okay,
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so here's what I'm gonna do. I'm gonna set
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x one to be ex X to to be ex
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prime x three to be why and then x four
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to be why prayer? So this first equation becomes
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three x two. Prime because X double crime plus
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five x one minus two x three equals zero.
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Then for the second equation, we have four x
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four Prime cause Why double Prime plus two x three
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minus six x one equals zero and then our final
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two differential equations actually relate Ex one next to in
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X three texts for and that's that x one prime
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is equal to X to and x three. Prime
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is equal to X for So there are four first
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order differential equations with our initial conditions. That x
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10 His negative one x 20 zero x three of
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zero is one and x 40 equals two. So
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we've converted these two second order differential equations and 24
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1st order, different equations.