Use the family in Problem 5 to find a solution of that satisfies the boundary conditions...

Use the family in Problem 5 to find a solution of that satisfies the boundary conditions

(reference problem 5)

Given that y = c₁ + c₂x² is a two-parameter family of solutions of on the interval show that constants c1 and c2 cannot be found so that a member of the family satisfies the initial conditions Explain why this does not violate Theorem 4.1.1.

(reference theorem 4.1.1)