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Let g(x) be the right side of a heterogeneous ODE. Why do we take the derivative of g(x) when using the method of undetermined coefficients? This is to guess the form of the particular solution.

The textbook says to assume the particular solutions includes both the terms of g(x) and their derivatives but doesn't answer why.

The textbook says to assume the particular solutions includes both the terms of g(x) and their derivatives but doesn't answer why.