(a) Verify that the one-parameter family y2 − 2y = x2 − x + c is an implicit solutio...

(a) Verify that the one-parameter family y² − 2y = x² − x + c is an implicit solution of the differential equation

(b) Find a member of the one-parameter family in part (a) that satisfies the initial condition y(0) = 1.

(c) Use your result in part (b) to find an explicit function that satisfies y(0) = 1. Give the domain of the function Is a solution of the initial-value problem? If so, give its interval I of definition; if not, explain.