Barrons AP Calculus

(a)

(b)

(a)

The slope field for the d.e. is shown in Figure N9–2.

Carefully   draw    the solution    curve   that    passes  through the point   (1, 0.5).

Find    the general solution    for the equation.

Figure  N9–2

SOLUTIONS:

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