- (a) Using the differential equation, evaluate the derivative at each point, then sketch a short segment
having that slope. For example, at (−1, −1), draw a segment at (−1, −1) that
decreases steeply. Repeat this process at each of the other points. The result is shown below.
(b) At (0, −1), For Δx = 0.5 and Δy = 0, so move to (0 + 0.5, −1 + 0) =
(0.5, −1).
At (0.5, −1), Thus, for Δx = 0.5 and Δy = 1.
Move to (0.5 + 0.5, −1 + 1) = (1,0), then f (1) ≈ 0.
(c) The differential equation is separable:
It is given that f passes through (0, −1), so −1 = tan(0^2 + c) and
The solution is
