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GATE 2022 MT – Question 36

Engineering Mathematics · Differential equations · 2 marks · Multiple choice

The general solution of $d^2y/dt^2-4dy/dt+4y=0$, with arbitrary constants $A,B$, is

  1. $y=A\sin(2t)+B$
  2. $y=A\sin(2t)+B\cos(2t)$
  3. $y=Ae^{2t}+Be^{-2t}$
  4. $y=Ae^{2t}+Bte^{2t}$

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Correct answer: (D) $y=Ae^{2t}+Bte^{2t}$

Explanation

The characteristic polynomial is $r^2-4r+4=(r-2)^2$. A repeated root 2 requires independent solutions $e^{2t}$ and $te^{2t}$.

Thus $y=Ae^{2t}+Bte^{2t}$, **D**.