Question: Write a differential equation that meets the given criteria: (a) A second-order differential equation that we could use a characteristic polyno- mial to solve. (b)

Write a differential equation that meets the given criteria: (a) A second-order differential equation that we could use a characteristic polyno- mial to solve. (b) A second-order differential equation that we would need the method of undeter- mined coefficients in order to solve. (c) A second-order differential equation for which neither a characteristic polyno- mial nor the method of undetermined coefficients would yield a solution. (d) Would the characteristic polynomial method work if applied to a first-degree homogeneous differential equation with constant coefficients? Explain why or why not

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