(a) By inspection find a one-parameter family of solutions of the differential equat...

(a) By inspection find a one-parameter family of solutions of the differential equation Verify that each member of the family is a solution of the initial-value problem y(0) = 0.

(b) Explain part (a) by determining a region R in the xy-plane for which the differential equation would have a unique solution through a point (x₀, y₀) in R.

(c) Verify that the piecewise-defined function

satisfies the condition y(0) = 0. Determine whether this function is also a solution of the initial-value problem in part (a).