SLOPE FIELDS
Draw a slope field for each of the following differential equations.
dy
dy
2. -=2y
1. -=x+I
dx
dx
.
.. .
.
•
._
.
t
•
.
•
.
.
•
•
.
•
-•
•
•
•
•
•
dy
3. -=x+y
dx
4.
dy
dx
=2x
•
•
•
dy
5. -=y-I
dx
.
.
y
dy
6. ---X
dx
•
Permission to use granted by Nancy Stephenson
Available at apcentraLcollegeboard_com_
.
.
•
•
.
--- ---
Match each slope field with the equation that the slope field could represent.
(A)
---1
---1
(B)
\--\---
--- -----
---1
---1
\--\---
(C)
(D)
_,_
-----�--------.,.. ____
-------------- ____
-----�---,,_
( E)
-
-
(G)
(F)
(H)
____ ...,___,
/✓--­
__ ...,___,
/✓--
1
x2
7. y=l
11. y=
8. y=x
12. y = sinx
9. y=x 2
13. y=cosx
1
10. y=-x 3
14. y = Inlxl
Permission to use granted by Nancy Stephenson
Available at apcentral.collegeboard.com.
Match the slope fields with their differential equations.
(A)
(B)
JI/ ✓
J J I/
/I I I
✓
/I/
/
(D) ,.......,...-,,-�-,,--......-,,--.---,,----,,-,
IIII
////
''''
\\\\
dy 1
15. -=-x+l
dx 2
dy
17. -=x-y
dx
dy
16. -=y
dx
dy
X
18. -=-dx
y
dy
= .xy is shown in
dx
the figure below. The solution curve passing through the point (0, 1) is also shown.
(a) Sketch the solution curve through the point (0, 2).
(b) Sketch the solution curve through the point ( 0, -1) .
19. The calculator drawn slope field for the differential equation
20. The calculator drawn slope field for the differential equation
the figure below.
(a) Sketch the solution curve through the point (0, 1).
(b) Sketch the solution curve through the point (-3, 0).
Permission to use granted by Nancy Stephenson
Available at apcentral.collegeboard.com.
dy
= x+ y is shown in
dx