Input ${\rm{x}}\left( {\rm{t}} \right)$ and output ${\rm{y}}\left( {\rm{t}} \right)$ of an LTI system are related by the differential equation ${\rm{y}"}\left( {\rm{t}} \right) - {\rm{y}'}\left( {\rm{t}} \right) - 6{\rm{y}}\left( {\rm{t}} \right){\rm{\;}} = {\rm{\;x}}\left( {\rm{t}} \right)$. If the system is neither causal nor stable, the impulse response h(t) of the system is

Question

Input ${\rm{x}}\left( {\rm{t}} \right)$ and output ${\rm{y}}\left( {\rm{t}} \right)$ of an LTI system are related by the differential equation ${\rm{y}"}\left( {\rm{t}} \right) - {\rm{y}'}\left( {\rm{t}} \right) - 6{\rm{y}}\left( {\rm{t}} \right){\rm{\;}} = {\rm{\;x}}\left( {\rm{t}} \right)$. If the system is neither causal nor stable, the impulse response h(t) of the system is

TuteeHUB · Accepted Answer

${\rm{\;}}\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)$

TuteeHUB · Answer

$\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) + \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right)$

TuteeHUB · Answer

$- \frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) + \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right)$

TuteeHUB · Answer

$- \frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)$

1.	Input \({\rm{x}}\left( {\rm{t}} \right)\) and output \({\rm{y}}\left( {\rm{t}} \right)\) of an LTI system are related by the differential equation \({\rm{y}"}\left( {\rm{t}} \right) - {\rm{y}'}\left( {\rm{t}} \right) - 6{\rm{y}}\left( {\rm{t}} \right){\rm{\;}} = {\rm{\;x}}\left( {\rm{t}} \right)\). If the system is neither causal nor stable, the impulse response h(t) of the system is
A.	\(\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) + \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right)\)
B.	\(- \frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) + \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right)\)
C.	\({\rm{\;}}\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)\)
D.	\(- \frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)\)
Answer» C. \({\rm{\;}}\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)\)

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