Find a linear second-order differential equation F(x, y, y', y'') = 0 for which y = c₁x + c₂x² is a two parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c₁ and c₂.

Qualitative information about a solution y = φ(x) of a differential equation can often be obtained from the equation itself. Before working Problems 55– 58, recall the geometric significance of the derivatives dy/dx and d²y/dx².