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GATE 2020 AE – Question 36

Engineering Mathematics · Differential Equations: First order linear ODEs and higher order linear ODEs with constant coefficients · 2 marks · Multiple choice

The equation $x\,dx/dy+y=c$, with constant c, represents a family of

  1. Exponential curves
  2. Parabolas
  3. Circles
  4. Hyperbolas

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Show answer and explanation

Correct answer: (C) Circles

Explanation

Rearrange as $x\,dx=(c-y)dy$ and integrate: $x^2/2=cy-y^2/2+C$. Completing the square gives $x^2+(y-c)^2=R^2$. Its nondegenerate real level curves are circles, C.

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