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4.3 Homogeneous Linear Equations with constant coefficients
by Elese Washines
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4.3 Homogeneous Linear Equations with constant coefficients

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auxiliary equation aka characteristic equation

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Case 1: Distinct Real Roots

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Case 2: Repeated Real Roots

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Case 3: Conjugate Complex Roots

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One way to solve homogeneous linear differential equations is by using differential operators and characteristic equations.