Adifferential equation may possess more than one family of solutions.
(a) plot different members of the families
_ _ 2 _ _ _ 2

y—¢i(x)-x +01 30d y—¢2(x)— x +02-
(b) verify that , y = ¢l(x) and y = ¢2(x) are two solutions of the nonlinear first-order differential equation
(3")2 = 4x2-
(c) construct a piecewise-defined function that is a solution of the nonlinear de in part (b) but is not a member of either
family of solutions in part (a)-