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GATE 2018 CE (CE2) – Question 11

Engineering Mathematics · ODE: First order and higher order linear equations, Euler-Cauchy equations, initial and boundary value problems · 1 mark · Multiple choice

The solution of $x\,dy/dx+y=0$ through (1,1) is ______.

  1. $x$
  2. $x^2$
  3. $x^{-1}$
  4. $x^{-2}$

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Correct answer: (C) $x^{-1}$

Explanation

Recognize $d(xy)/dx=xy^\prime+y=0$, hence $xy=C$. The point (1,1) gives C = 1, so $y=x^{-1}$ on the interval containing x = 1 (C).