Use the family in Problem 5 to find a solution of xy'' – y' =­ 0 that satisfies the boundary conditions y(0) =­ 1, y'(1) =­ 6.

Data from problem 5

Given that y ­= c₁ + c₂x² is a two-parameter family of solutions of xy'' – y' =­ 0 on the interval (‑∞, ∞), show that constants c₁ and c₂ cannot be found so that a member of the family satisfi­es the initial conditions y(0) ­= 0, y'(0) ­= 1. Explain why this does not violate Theorem 4.1.1.