Question: Consider the differential equation ay'' + by' + cy = g(x), where a, b, and c are constants. Choose the input functions g(x) for which

Consider the differential equation ay'' + by' + cy = g(x), where a, b, and c are constants. Choose the input functions g(x) for which the method of undetermined coefficients is applicable and the input functions for which the method of variation of parameters is applicable.

(a) g(x) = e^x lnx

(b) g(x) = x³ cosx

(d) g(x) = 2x^-2e^x

(e) g(x) = sin²x

(f) g(x) = e^x/sin x

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