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1. y"-8y'+25y=0
2. y"+5y'+6y=0
3. y"-2y'+y=0
1. y"-8y'+25y=0
2. y"+5y'+6y=0
3. y"-2y'+y=0
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1. a² - 8a + 25 = 0
D = 64 - 100 = 36i²
a₁ = 4 + 3i
a₂ = 4 - 3i
y = e⁴ˣ(C₁cos3x + C₂sin3x)
2) a² + 5a + 6 = 0
D = 25 - 24 = 1
a₁ = -3
a₂ = -2
y = C₁e⁻²ˣ + C₂e⁻³ˣ
3. a² - 2a + 1 = 0
(a - 1)² = 0
a₁₂ = 1
y = C₁eˣ + C₂xeˣ