WEBVTT
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first, I want to verify that this has a
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initial value of while pipe will zero. So we're
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just gonna plug in pie for every t value.
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So negative pine times coast on a pie minus pi
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. I don't want this equal zero. So cousin
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pie is the quadrants of angle pies. Located here
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does zero. I have high and three pie,
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perhaps, and pies Here this coordinate is negative 10
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and that's co sign sign. So comes on in
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these cases, negative one. Still have zero equals
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negative pi times negative one because co Santa pies negative
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points all minus pi. So zero equals in a
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negative times negative gives us a positive pot and anything
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might it still is zero. So this initial condition
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checks out, we also need to verify that it
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is so It is a solution of this equation here
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. So what we have to do is we have
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to play in our derivative and we have to plug
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in our original Why equation? So our suspect,
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the derivative of our y equations. So we have
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d y B c equals the first times the derivative
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of the second, which is negative, scientific,
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close the second times, the derivative of the first
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, which is negative point. And then the river
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of, uh, minus T that's just minus one
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. So we simplify. This will have the positive
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t Sorrenti minus a co sign T minus one.
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Just most applied everything together and we simplified. So
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this is far as we can simplify the situation.
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Now we need to plug in our were C Y
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d T equation in our Y collision. So have
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I t times t sai Inti minus co sign T
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minus one. Now, when this starts equals,
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we're gonna play guitar y equation. Our original migration
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here. So we had negative t co sign t
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minus t and we bring down our plus t squared
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sine ti. So now we distribute owner left side
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will have t squared sign T minus t co sci
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fi minus E on left side, on the right
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side. We don't have anything to distribute, So
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we're just gonna bring everything down. If you look
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on the left hand side, it matches our right
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hand side. We have everything. We have a
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t squared Zion T we have a minus. Seiko
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Cy Inti and we have a minus t. So
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since our looks inside, it was our right hand
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side. We have verified that these solutions