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de1sample - Diﬀerential Equations Test 1 sample Answer...

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Unformatted text preview: Diﬀerential Equations Test 1 sample Answer FOUR questions. Show all working clearly. 1. Solve the initial value problem dy 2x = , dx 1 + 2y y (0) = 0. 2. Solve the initial value problem x dy + 2y = sin x, dx y (π/2) = 0. 3. Find k so that the diﬀerential equation y dx − xdy =0 (x2 + y 2 )k is exact and solve it with this value. 4. Solve either (a) or (b): (a) 2xy dy = x2 + 3y 2 ; dx dy − xy = 5xy 2 . dx 5. A population N grows logistically and is harvested at constant rate, so that dN N = rN (1 − ) − h dt K where K , r and h are positive constants. Show that if h < Kr/4 then there are two equilibrium solutions for N . What happens to H as t → ∞ if h > Kr/4? (b) (1 − x2 ) 1 ...
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This note was uploaded on 11/12/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.

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