BC ONLYC. EULER’S METHOD
In §B we found solution curves to first-order differential equations graphically,
using slope fields. Here we will find solutions numerically, using Euler’s method
to find points on solution curves.
When we use a slope field we start at an initial point, then move step by step
so the slope segments are always tangent to the solution curve. With Euler’s
method we again select a starting point; but now we calculate the slope at that
point (from the given d.e.), use the initial point and that slope to locate a new
point, use the new point and calculate the slope at it (again from the d.e.) to
locate still another point, and so on. The method is illustrated in Example 6.