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Solve $(D - 1)^2 (D^2 + 1) y = 0$

written 9.5 years ago by teamques10 ★ 70k

modified 3.9 years ago by phenjoisilab • 0

engineering mathematics

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written 9.5 years ago by teamques10 ★ 70k

Auxiliary equation is $(D - 1)^2 (D^2 + 1) y = 0$

$(D - 1)^2 = 0$ or $(D^2 + 1) = 0$

$D = 1, 1$ or $D^2 = -1 = i^2$

$D = 1,1$ or $0 = \pm1$

Complementary function is

$Y_c = (C_1 + xC_2)e^x + e^{Dx} (C_{3\cos x} + C_{4\sin x})$

$Y_c = (C_1 + xC_2)e^x + C_{3\cos x} + C_{4\sin x}$

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