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KCET2008MathematicsDifferential Equations

The differential equation y d y d x +x= crepresents

Options

  1. Aa family of hyperbolas
  2. Ba family of circles whose centres are on the axis
  3. Ca family of parabolas
  4. Da family of circles whose centres are on the axis

Correct answer

D. a family of circles whose centres are on the axis

Step-by-step solution

Given differential equation is aligned y d y d x +x &=c y d y &=(c-x) d x aligned On integrating both sides, we get aligned y² 2 &=c x- x² 2 +d y²+x²-2 c x-2 d &=0 aligned Hence, it represents a family of circles whose centres are on the x -axis.

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