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KCET2009MathematicsDifferential Equations

The differential equation of the family of circles passing through the orign and having their centres on the x -axis is

Options

  1. Ay ²= x ²+2 xy dy dx
  2. By²=x²-2 x y d y d x
  3. Cx²=y²+x y d y d x
  4. Dx²=y²+3 x y d y d x

Correct answer

A. y ²= x ²+2 xy dy dx

Step-by-step solution

The system of circles passing through origin and centre lies on x -axis is x ²+ y ²-2 h x =0 ...(i) On differentiating w.r.t. x , we get aligned &2 x +2 y dy dx -2 ~h =0 & 2 x +2 y dy dx - ( x ²+ y ² x )=0 [from Eq. (i)] & x ²- y ²+2 xy dy dx =0 aligned

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