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COMEDK2019MathematicsDifferential Equations

The differential equation y d y d x +x=c represents

Options

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

Correct answer

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

Step-by-step solution

We have, gathered y d y d x +x=c y d y d x =(c-x) y d y=(c-x) d x gathered array ll & y d y=-(x-c) d x & y d y=- (x-c) d x & y² 2 =- (x-c)² 2 +K & (x-c)²+y²=2 K array which is a circle with centre (c, 0) on the X -axis.

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