Direction Field Example

(A complete intro to direction fields is in Chapter 1.1)

Given the F.O.L.:

y' + 2ty = t

If we solve it, we find that its solutions are of the form

$$y(t) = \frac{1}{2} + ce^{-t^2}$$

We can get an idea of what these solutions look like from the direction field of the differential equation:

[Figure 2.1.4 and 2.1.5 complete this slide]