approximates the family of solutions.
FIGURE N9–1cEXAMPLE 2
The slope field for the d.e. is shown in Figure N9–2.
(a) Carefully draw the solution curve that passes through the point (1, 0.5).
(b) Find the general solution for the equation.
FIGURE N9–2
SOLUTIONS:
(a) In Figure N9–2a we started at the point (1, 0.5), then moved from segment to segment
drawing the curve to which these segments were tangent. The particular solution curve shown
is the member of the family of solution curves
y = ln x + C
that goes through the point (1, 0.5).
FIGURE N9–2a