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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.
 Fall '08
 TUNCER

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