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in Differential Equations by (120 points)
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Solve the differential equation \[ y^{\prime \prime \prime}(t)+2 y^{\prime \prime}(t)+y^{\prime}(t)=0 \]

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1 Answer

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by (45.0k points)

It's auxiliary equation is 

m3 + 2m2 + m = 0

⇒ m(m2 + 2m + 1) = 0

⇒ m(m + 1)2 = 0

⇒ m = 0, -1, -1

∴ y = C.F. = C1e0x + (C2 + C3x)e-x

⇒ y = C+ (C2 + C3x)e-x which is solution of given differential equation.

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