Consider the differential equation dy dt

= −y 2

.

a. Find a one-parameter family of solutions (i.e., a formula for solutions, with one arbitrary constant in the formula).

b. Check that you have the correct answer in

(a) by substituting your answer back into the differential equation.

c. Calculate the solution with y(0) = A, where A < 0. For what range of t does this solution exist? (Don’t forget to include both positive and negative t.)

d. Describe what happens to the solution as it approaches the limit of its domain of definition. Why can’t the solution be extended for more time?

e. How does the solution behave if A > 0?