As an illustration of the difficulties that may arise in using the method of undetermined coefficients, consider х + Form the complementary solution to the homogeneous equation. 1 e^(2t) help (formulas) x.(t) = c1 + C2 help (matrices) -1 e^(2t) Show that seeking a particular solution of the form x,(t) = e2"ā, where a = is a constant vector, does not work. In fact, if x, had this form, we would arrive at the following contradiction: a1 help (numbers) and • aj help (numbers) Show that seeking a particular solution of the form xp(t) = te2 ā, where a is a a2 constant vector, does not work either. In fact, if x, had this form, we would arrive at the following contradiction: • aj help (numbers) and aj = help (numbers) and a, = help (numbers)

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