Let a causal LTI system be characterized by the following differential equation, with initial rest condition {d^{2}y}/{dt^{2}} + 7\frac{dy}{dt} + 10y (t) = 4x (t) + 5\frac{dx (t) }{dt} where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

Correct Answer is : –2e-2tu(t) + 7 e-5tu(t)

GATE Electrical Engineering (EE) 2017 Shift 1 Solved Paper

Question : 40 of 65

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Let a causal LTI system be characterized by the following differential equation, with initial rest condition

\;{d^{2}y}/{dt^{2}} + 7\;{dy}/{dt} + 10y (t) = 4x (t) + 5\;{dx\;(t)\;}/{dt}

where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

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