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GATE 2014 EC (EC1) – Question 55

Control Systems · Transient and Steady-State Analysis of LTI Systems · 2 marks · Multiple choice

A system obeys $\dot y(t)+5y(t)=u(t)$. With y(0) = 1 and unit-step input u(t), find y(t).

  1. $0.2+0.8e^{-5t}$
  2. $0.2-0.2e^{-5t}$
  3. $0.8+0.2e^{-5t}$
  4. $0.8-0.8e^{-5t}$

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Correct answer: (A) $0.2+0.8e^{-5t}$

Explanation

For t≥0, y′+5y=1 has particular solution1/5 and homogeneous solution Ce⁻⁵ᵗ. The initial condition y(0)=1 gives C=4/5. Therefore **y(t)=0.2+0.8e⁻⁵ᵗ,A**. This satisfies both the initial value and the steady-state value0.2.