(A) The slope segments are not parallel in either the x or y direction, so
the d.e. must include both x and y in the definition; this excludes (C) and
(D). (B) will have zero slopes along the x-axis, so we can eliminate (B).
Finally, both (A) and (E) will have zero slopes along the y-axis, (E) will
also have zero slopes at (1, −1) and (−1, −1), eliminating (E). (Note: (A)
will have zero slopes at (1, −1) and (−1, 1).)
(E) The slope segments are parallel horizontally meaning that the slopes
don’t change as x varies; therefore, the d.e. is defined by the y-coordinate
only. This excludes (A), (B), and (C). Choice (D) will have zero slopes
along the x-axis, whereas (E) will never have zero slopes; thus (E) will
create this slope field.
(D) We separate variables to get . We integrate:
(B) Since , dt, and ln R = ct + C. When t = 0, R = R 0 ; so ln R 0
= C or ln R = ct + ln R 0 . Thus
(D) The question gives rise to the differential equation , where P =
2 P 0 when
