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354 Chapter 6: Differential Equations
6.1 Slope Fields and Euler’s Method
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which of the following is a solution of the differential equation ?
a.
b.
c.
d.
e.
____ 2. Which of the following is a solution of the differential equation ?
a.
b.
c.
d.
e.
____ 3. Which of the following is a solution of the differential equation ?
a.
b.
c.
d.
e.
____ 4. Find the particular solution of the differential equation that satisfies
the initial condition when x = 2, where is the general solution.
a.
b.
c.
d.
e.
6.1 Slope Fields and Euler’s Method 355
____ 5. Use integration to find a general solution of the differential equation.
a.
b.
c.
d.
e.
____ 6. Use integration to find a general solution of the differential equation.
a.
b.
c.
d.
e.
____ 7. Use integration to find a general solution of the differential equation .
a.
b.
c.
d.
e.
356 Chapter 6: Differential Equations
____ 8. Use integration to find a general solution of the differential equation
.
a.
b.
c.
d.
e.
____ 9. Use integration to find a general solution of the differential equation.
a.
b.
c.
d.
e.
____ 10. Use integration to find a general solution of the differential equation.
a.
b.
6.1 Slope Fields and Euler’s Method 357
c.
d.
e.
____ 11. Use integration to find a general solution of the differential equation .
a.
b.
c.
d.
e.
____ 12. Use integration to find a general solution of the differential equation.
a.
b.
c.
d.
e.
358 Chapter 6: Differential Equations
____ 13. Use the differential equation and its slope field to find the slope at the point
.
a. 32
b. 1
c. 8
d. 64
e. 16
6.1 Slope Fields and Euler’s Method 359
____ 14. Select from the choices below the slope field for the differential equation.
a. d.
b. e. none of the above
c.
360 Chapter 6: Differential Equations
____ 15. Select from the choices below the slope field for the differential equation.
a. c.
b. d. none of the above
6.1 Slope Fields and Euler’s Method 361
____ 16. Select from the choices below the slope field for the differential equation.
a. d.
b. e. none of the above
c.
362 Chapter 6: Differential Equations
____ 17. Identify the slope field of the differential equation .
a. d.
b. e.
c.
6.1 Slope Fields and Euler’s Method 363
____ 18. Sketch the slope field for the differential equation and use the slope field
to sketch the solution that passes through the point .
a.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
d.
b.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
e.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
c.
12345–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
364 Chapter 6: Differential Equations
____ 19. Sketch the slope field for the differential equation and use the slope field
to sketch the solution satisfying the condition .
a. d.
b. e.
c.
6.1 Slope Fields and Euler’s Method 365
____ 20. Use Euler's Method to make a table of values for the approximate solution of the
following differential equation with specified initial value. Use 5 steps of size 0.15.
a.
b.
c.
d.
e.
____ 21. At time minutes, the temperature of an object is . The temperature of the
object is changing at the rate given by the differential equation . Use Euler's
Method to approximate the particular solutions of this differential equation at . Use a step size of
. Round your answer to one decimal place.
a. 96.6
b. 99.9
c. 102.9
d. 98.1
e. 97.4
366 Chapter 6: Differential Equations
6.1 Slope Fields and Euler’s Method
Answer Section
