Question: If a system is represented by the differential equation ; [ frac{d^{2} y}{d t^{2}}+frac{6 d y}{d t}+9 y=0 ] then the solution (mathrm{y}) will be

If a system is represented by the differential equation ;
\[
\frac{d^{2} y}{d t^{2}}+\frac{6 d y}{d t}+9 y=0
\]
then the solution \(\mathrm{y}\) will be of the form:
(a) \(k_{1} e^{-t}+k_{2} e^{-9 t}\)
(b) \(\left(k_{1}+k_{2} tight) e^{-3 t}\)
(c) \(k e^{-3 t} \sin (t+\phi)\)
(d) \(\left(k_{1}+k_{2} tight) e^{3 t}\)

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