(a) What can you say about the graph of a solution of the equation y’ = xy3 when is close to 0? What if is large?
(b) Verify that all members of the family y = (c – x2)–½ are solutions of the differential equation y’ = xy3.
(c) Graph several members of the family of solutions on a common screen. Do the graphs confirm what you predicted in part (a)?
(d) Find a solution of the initial-value problem y’ = xy3 y (0) = 2