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GATE 2025 IN – Question 12

Engineering Mathematics · Differential equations · 1 mark · Multiple choice

The solution of the differential equation $dy/dx=9x/y$ represents

  1. a hyperbola
  2. a parabola
  3. an ellipse
  4. a circle

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Correct answer: (A) a hyperbola

Explanation

Separate variables: y dy=9x dx.

Integration gives y²−9x²=C, a family of hyperbolas for nonzero C, with a degenerate pair of lines when C=0.

The intended curve class is **hyperbola, A**.