Consider a causal LTI system characterized by differential equation \frac{dy (t) }{dt} + \frac{1}{6}y (t) = 3x (t). The response of the system to the input x (t) = 3e^{−\frac{t}{3}u (t) }. Where u(t) denotes the unit step function is

Correct Answer is : 54−t6u(t)−54e−t3u(t)

9e^{−\frac{t}{3}}u (t) −6e^{−\frac{t}{6}}u (t)

54^{−\frac{t}{6}}u (t) −54e^{−\frac{t}{3}}u (t)

GATE Electrical Engineering (EE) 2016 Shift 2 Solved Paper

Question : 14 of 65

Marks: +1, -0

Consider a causal LTI system characterized by differential equation

\;{dy\;(t)\;}/{dt} + \;{1}/{6}y (t) = 3x (t)

. The response of the system to the input

x (t) = 3e^{−\;{t}/{3}u (t) }

. Where u(t) denotes the unit step function is

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