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MATH 20D  Practice Exam #1
The exam covers Sections 1.13.2 (inclusive) minus 2.8 and 2.9
closed book, no calculators, no computers, no notes, no headphones .
..
each problem is worth the same number of points
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1)
a)
Find an integrating factor u
for
y’  xy = x.
b)
Solve the ODE in part a) by multiplying it by the integrating factor
u and recognizing the left hand side as (uy)’.
2)
Solve the separable ODE
y y’
+ x
= 0
with initial condition
y(2)=2.
Find the interval a
≤
x
≤
b
where the solution y(x) is defined.
If you were to plot the direction field, what would you
expect to see?
3)
A tank contains 100 gallons of salty water made by dissolving 80 lb. of salt in water.
Pure
water runs into the tank at the rate of 4 gal./min,
and the wellstirred mixture runs out at
the same rate.
Let Q(t) be the
amount of salt in the tank at time t.
a)
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 Spring '09
 staff
 Math, Boundary value problem, Lipschitz continuity

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