Q: What is the general solution of a homogeneous differential equation with the characteristic equation λ³(λ + 4)²(λ² + 2λ + 5)² = 0?
(a)y(x) = c₁ + c₂x + c₃x² + c₄e⁻⁴ˣ + c₅xe⁻⁴ˣ + eˣ{c₆ cos 2x + c₇ sin 2x} + c₈x cos 2x + c₉x sin 2x
(b)y(x) = c₁ + c₂x + c₃x² + c₄e⁻⁴ˣ + c₅xe⁻⁴ˣ + e⁻ˣ{c₆ cos 2x + c₇ sin 2x} + eˣ{c₈x cos 2x + c₉x sin 2x}
(c)y(x) = c₁ + c₂x + c₃x² + c₄e⁻⁴ˣ + c₅xe⁻⁴ˣ + eˣ{c₆ cos 2x + c₇ sin 2x} + e⁻ˣ{c₈x cos 2x + c₉x sin 2x}
(d)y(x) = c₁ + c₂x + c₃x² + c₄e⁻⁴ˣ + c₅xe⁻⁴ˣ + e⁻ˣ{c₆ cos 2x + c₇ sin 2x} + xe⁻ˣ{c₈ cos 2x + c₉ sin 2x}
Correct Answer: (d)
Detailed explanation coming soon.