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posted by  Norby on 8/24/2008 9:30:13 PM  |  status: Closed  

Differential Equation. Lifesaver!

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Find the general solution of the differential equation:

y'''+2y''+y'+2y=0
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posted by Altair on 8/24/2008 10:38:05 PM  |  status: Live
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Response Details:
m3 + 2m2 + m + 2 = 0
 
m(m2+1) + 2(m2+1) = 0
(m+2)(m2 + 1) = 0
 
m=-2, -i, i
 
the general solution is:
 
y = c1 e-2x + c2 cosx + c3 sinx   (or c1 e-2x + c2e-ix + c3 eix)
 
 

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