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[!]
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[=post-]
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<p>
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<i>This post is part of a series; you can view the next post <a href="[^baseurl]/posts/differential-exam-1.html">here</a>.</i>
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</p>
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<p>
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Welcome once more to Deadly Boring Math! With the tempestuous wight of Quiz 2 rapidly striding towards us (it's <i>tomorrow</i> in the usual studio time),
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I'm doing some last-minute studying, and figured I'd post some worked solutions here. These are by no means exhaustive; if you don't do your own studying,
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<p>
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The first step is to define some substitutions: `x = u`, `y = u'`, meaning `x' = u'`, and `y' = u''`. Note also that `x' = y`.
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Substituting these values into the equation gives us `y' - 2y + x = sin(t)`: because we have the constraint `x' = y`, this is
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a system of equations. We do some algebra to get `y' = 2y - x + sin(t), x' = y`, which can be written in matrix form as `X' = \[\[0, 1], \[-1, 2]] X + [0, sin(t)]`.
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a system of equations. We do some algebra to get `y' = 2y - x + sin(t), x' = y`, which can be written in matrix form as `X' = \[\[0, 1], \[-1, 2]] X + \[0, sin(t)]`.
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</p>
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<h2>WS3.3.1</h2>
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<p>
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[=title "Differential Quiz 2"]
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[=subject "Calculus"]
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[=author "Tyler Clarke"]
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[=date "2025-6-2"]
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[=date "2025-6-2"]
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[#post.html]
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