5 Steps to a 5 AP Calculus BC 2019

326 STEP 4. Review the Knowledge You Need to Score High

Example 3

A slope field for a differential equation is shown in Figure 13.5-3. Draw a possible graph

for the particular solutiony= f(x) to the differential equation function, if (a) the initial

condition isf(0)=−2 and (b) the initial condition isf(0)=0.

Figure 13.5-3

Solution:

Begin by locating the point (0,−2) as given in the initial condition. Follow the flow of the

field and sketch the graph of the function. Repeat the same procedure with the point (0, 0).

See the curves as shown in Figure 13.5-4.

Figure 13.5-4

Example 4

Given the differential equation

dy

dx

=−xy:

(a) Draw a slope field for the differential equation at the 15 points indicated on the

provided set of axes in Figure 13.5-5.

3

2

1

–2 0–1 1 2

y

x

Figure 13.5-5