Math 1320 Lab 3
Name/Unid:
1. Solve the following differential equations.
dy
(a)
= x2 y − x2 .
dx
(b)
dy
= 6x(y − 1)2/3 ,
dx
y(0) = 1.
2. Match each differential equation with the corresponding vector field. For each slope
field, sketch a few likely solution curves.
Differential equations:
x−1
dy
=
dx
y
dy
= y − sin x
2.
dx
1.
dy
= x2 + y 2 − 1
dx
dy
= x2 + 1
4.
dx
3.
Vector fields:
(a)
(c)
(b)
(d)
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3. A glass of hot water is cooling down with surrounding temperature constant at 70 F.
The time rate of change of the water temperature x(t) is proportional to the difference
between x(t) and the surrounding temperature. Suppose that the water temperature is
100 F at first and drops to 80 F after 10 minutes.
(a) Find the differential equation that describes the water temperature x(t).
(b) Find the solution of the differential equation you derived in part (a).
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4. When a raindrop falls, it increases in size and so its mass at time t is a function of t,
namely m(t). The rate of growth of the mass is km(t) for some positive constant k.
When we apply Newton’s Law of Motion to the raindrop, we get (mv)0 = gm, where
v is the velocity of the raindrop (directed downward) and g is the acceleration due to
gravity. The terminal velocity of the raindrop is limt→∞ v(t). Find an expression for the
terminal velocity in terms of g and k.
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