BC Calculus: Ch.6
REVIEW: “Differential Equations”
NAME ____________________
DATE __________ PER _____
1) One of the following slope fields is for the differential equation
other is for the differential equation
y
dy
 cos  xy and the
dx
dy
 sin  xy .
dx
y
x
x
B
A
a) Which slope field goes with which equation? How can you tell?
b) Explain how the behavior of the slope lines along the axes helps to identify the correct
equation.
c) Explain how the symmetry of the graph helps to identify the correct equation.
#2-5 A differential equation, a point, and a slope field are given. Sketch an approximate
solution of the differential equation on the slope field, which passes through the given point.
Solve the differential equation for the particular solution.
x
2)
dy
 0.4 3 ,
dx
 1
 0, 
 2
y
 , 2
dy
 e sin x cos x ,
dx
3)
y
x
x
4)
dy
3

,
dx
1  x2
0, 0
5)
dy

dx
2
25  x 2
,
5, 
y
y
x
x
6) Use Euler’s Method, with h = 0.1, to estimate y (0.5) if y '  y  1 and y (0)  3 .
7) Use Euler’s Method, with h = 0.2, to estimate y (2) if y '  2 y  1 and y (1)  5 .
8) If
dy
  10 y and if y  50 when x  0 , find y .
dx
9) Find the general solution to the first order differential equation 2 x( y  1)  y y '  0 .
10) Solve the differential equation y'  x 2 with the initial condition y (0)  2 .
From your solution, find the value of y (1) .
11) An object cools at a rate (measured in °C per minute) equal to k times the difference
between its temperature and that of the surrounding air. Suppose the object takes 10 minutes
to cool from 60° to 40°C in a room kept at a constant 20°C. What is the value of k.
12) A particle moves on the x-axis so that at any time t its velocity v(t )  sin (2t ) is subject
to the condition x(0)  0 where x(t ) is the position function. Write an expression for x(t ) .
13) An object cools at a rate (measured in °C per minute) equal to 0.1 of the difference
between its temperature and that of the surrounding air. If a room is kept at 20°C and the
temperature of the object is 28°C, what is the approximate temperature (in Celsius) of the
object 5 minutes later?
Review your notes and assignments. Study for your TEST!
Solutions: