(d2 - 3d + 2)y = 0, where D = d/dx is _____

1.	(d2 - 3d + 2)y = 0, where D = d/dx is _____
Answer» (D² – 3D + 2)y = 0 It's auxilarly equation is m² – 3m + 2 = 0 ⇒ m² – 2m – m + 2 = 0 ⇒ m(m – 2) – 1(m – 2) = 0 ⇒ (m – 2)(m – 1) = 0 ⇒ m = 1, 2 Therefore, its solution is y = C₁e^x + C₂e^2x.

Answer»

(D² – 3D + 2)y = 0

It's auxilarly equation is

m² – 3m + 2 = 0

⇒ m² – 2m – m + 2 = 0

⇒ m(m – 2) – 1(m – 2) = 0

⇒ (m – 2)(m – 1) = 0

⇒ m = 1, 2

Therefore, its solution is y = C₁e^x + C₂e^2x.

Discussion

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