Use qualitative methods (Modified Euler's, Harvesting or LogisticMethods) to sketch the solution to the initial value problem:

dy=y2, y(0)=1 dt 4

Your answer should include:

steady-state solutions.

• The graph of y vs. y with stability arrows is drawn.
• The stability of steady-state(s) labeled.
• The solution curve, y(t) vs t.
• If applicable, clear indications of any asymptotic behavior, concavity, and points of inflection.

(b) Use separation of variables to solve the initial value problem in part (a).

Observe that the solution has a vertical asymptote at t = 4. Draw a vertical dashed line at t = 4 to highlight the vertical asymptote. This phenomenon is called blow-up because the solution becomes infinite in a finite time. Note that the blow-up cannot be predicted by qualitative methods (done in part (a)).