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Lecture15 - Announcements* today* Thisweek Topics...

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Announcements ** Test 1 will be available for pick up in the Math Help Centre today ** Test 2 this Thursday – See webpage for details This week: Topics: ‐ Separable DEs ‐ Linear DEs ‐ Predator/Prey Model Work On: ‐ Finish Assignment 5 ‐ Finish PracMce Problems Set 5 and Set 6
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Separable EquaMons A separable equa+on is a first‐order differenMal equaMon in which the expression for dy/dx can be factored (or “separated”) as a funcMon of x Mmes a funcMon of y. In other words, it can be wriZen in the form dy dx = g ( x ) f ( y )
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Separable EquaMons It is possible to find an algebraic soluMon (formula for y(x)) for these types of DEs. To solve this equaMon, first rewrite it in the differen+al form so that all y’s are on one side of the equaMon and all x’s are on the other side. h ( y ) dy = g ( x ) dx where h ( y ) = 1 f ( y )
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Separable EquaMons Next, integrate both sides of the equa+on
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