Find a linear second-order differential equation for which y = c1x + c2x2 is a twoparame...

Find a linear second-order differential equation for which y = c₁x + c₂x² is a twoparameter family of solutions. Make sure that your equation is free of the arbitrary parameters c₁ and c₂.

Qualitative information about a solution of a differential equation can often be obtained from the equation itself. Before working Problems 55– 58, recall the geometric significance of the derivatives and