We will investigate the initial-value problem y' = y2, y(0) = 1.
(a) Show that Picard's conditions hold. How large a region R can be found?
(b) Draw the direction field and solution.
(c) Solve the IVP using separation of variables. What is the largest t-interval for which this solution is defined? How does it compare with the region R of pan (a)?
(d) Generalize the results of parts (a) and (c) to the IVP y' = y2 ∙ y(t0) = y0