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QUESTION

Find the general solution of the differential equation
$\ds\frac{d^2x}{dt^2}+5\frac{dx}{dt}+6x=0$.

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ANSWER

$\ds\frac{d^2x}{dt^2}+5\frac{dx}{dt}+6x=0.$ The auxiliary equation
is $m^2+5m+6=0=(m+3)(m+2),$ which has solutions $m=-2,-3.$
Therefore $x=Ae^{-2t}+Be^{-3t}$.



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