Discussion
Consider the following statements about particular integrals. 1. A factor of \( x \) is needed when the forcing term solves the homogeneous equation 2. The operator method handles \( \ln x \) directly 3. Variation of parameters needs the complementary function first
Answer: D
The resonant case does need the extra factor, and variation of parameters does build the particular integral from the complementary solutions, so it cannot be attempted first. A logarithm is outside the operator method's repertoire, which covers exponentials, sinusoids, polynomials and their products
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