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GATE 2014 EC (EC4) – Question 14

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

If a,b are constants, find the most general solution of $d^2x/dt^2+2dx/dt+x=0$.

  1. $ae^{-t}$
  2. $ae^{-t}+bte^{-t}$
  3. $ae^t+bte^{-t}$
  4. $ae^{-2t}$

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Correct answer: (B) $ae^{-t}+bte^{-t}$

Explanation

The characteristic polynomial is r²+2r+1=(r+1)². A repeated root−1requires two independent solutions e⁻ᵗand te⁻ᵗ. Therefore the general solution is **ae⁻ᵗ+bte⁻ᵗ,B**, with two arbitrary constants.