Barrons AP Calculus - David Bock

y 3 = y 2 + Δy = 2.5 + 0.75 = 3.25,

P 3 = (2.5, 3.25),

and so on.
The table summarizes all the data, for the four steps specified, from x = 1 to x = 3:

TABLE FOR

The table gives us the numerical solution of using Euler’s method. Figure N9–6a shows the
graphical solution, which agrees with the data from the table, for x increasing from 1 to 3 by four
steps with Δx equal to 0.5. Figure N9–6b shows this Euler graph and the particular solution of
passing through the point (1,0), which is y = 3 ln x.

FIGURE N9–6a