Barrons AP Calculus - David Bock

FIGURE N9–3c

FIGURE N9–3d
SOLUTIONS:
(A) goes with Figure N9–3c. The solution curves in the family y = sin x + C are quite obvious.

(B) goes with Figure N9–3a. The general solution is the family of parabolas y = x^2 + C.
For (C) the slope field is shown in Figure N9–3b. The general solution is the family of cubics y
= x^3 − 3x + C.
(D) goes with Figure N9–3d; the general solution is the family of lines y =

EXAMPLE 4

(a) Verify that relations of the form x^2 + y^2 = r^2 are solutions of the d.e.

(b) Using the slope field in Figure N9–4 and your answer to (a), find the particular solution to the

d.e. given in (a) that contains point (4, −3).

FIGURE N9–4