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AP Calculus Problem Set 43
1/6/12
Upon completion, circle one of the following to assess your current understanding:
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1. Find the particular solution y  f  x  to the given differential equation with the initial condition f  2  1
dy
x 1
 3
dx
2y
2. Find the particular solution y  f  x  to the given differential equation with the initial condition f 1  4
dy 3x 2  1

dx
2y
3. Find the particular solution y  f  x  to the given differential equation with the initial condition f  3  25
dy
x y
dx
4. Find the particular solution y  f  x  to the given differential equation with the initial condition f  1  2
dy  xy 2

dx
2
5. Find the particular solution y  f  x  to the given differential equation with the initial condition f 1  1
dy
2x

dx
y
6. Find the particular solution y  f  x  to the given differential equation with the initial condition f 1  0
dy
2
  y  1 cos  x 
dx
7. Find the particular solution y  f  x  to the given differential equation with the initial condition f  0   2
dy x  1

dx
y
8. Find the particular solution y  f  x  to the given differential equation with the initial condition f 1  2
dy
 xy 3
dx
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9. Find the particular solution y  f  x  to the given differential equation with the initial condition f  6   4
dy 3  x

dx
y
10. Find the particular solution y  f  x  to the given differential equation with the initial condition f  3 
1
4
dy
 y2 6  2x
dx
11. Find the particular solution y  f  x  to the given differential equation with the initial condition f 1  2
dy  5 x  3

dx
y2
4
12. Find the particular solution y  f  x  to the given differential equation with the initial condition f  8  2
dy
43 x

dx sin  y 
13. Find the particular solution y  f  x  to the given differential equation with the initial condition f  2  9
dy 6 x 2  x

dx
y
14. Given h  5 at time t  0 where h is the height, in inches, of the water in a container and t is the time, in
minutes, solve the differential equation
dh
h3
for h as a function of t .

dt
4
15. Given h  64 at time t  3 where h is the height, in feet, of the water in the center of a lake and t is the
time, in days, solve the differential equation
dh
 2t
dt
3
h for h as a function of t .
16. Let v  t  be the velocity, in feet per second, of an elevator at time t seconds. The velocity of the
dv  2t  3

elevator satisfies the differential equation
with initial condition v 1  0 . Find an
dt
sin v
expression for v in terms of t.
3
17. Let v  t  be the velocity, in meters per second, of a skydiver at time t seconds. The velocity of the
skydiver satisfies the differential equation
for v in terms of t.
dv 5

with initial condition v 1  2 . Find an expression
dt v 3