32. Verify that if c> 0, then the function defined piecewise

by

= {²-

if x² ≤ c.

(x²-c)² if x² >c

y(x) =

satisfies the differential equation y'= 4x√√y for all x.

Sketch a variety of such solution curves for different val-

ues of c. Then determine (in terms of a and b) how many

different solutions the initial value problem y' = 4x√y.

y(a) = b has.