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QUESTION

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


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ANSWER

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




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