Find a linear second order differential equation F(x, y, y ', y ' ') 0 for which y c 1 x c 2 x 2 is a two parameter family of solutions Make sure that your equation is free of the arbitrary parameters c 1 and c 2 Qualitative information about a solution y (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 d 2 y dx 2

Question: Find a linear second-order differential equation F(x, y, y', y'') = 0 for which y = c 1 x + c 2 x 2 is

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.

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