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AP EAMCET · Maths · Differential Equations

The differential equation of the family of circles passing through the origin and having centre on X -axis is

  1. A \(\left(y^2+x^2\right) d x-2 y d y=0\)
  2. B \(\left(y^2-x^2\right) d x-2 x y d y=0\)
  3. C \(\left(y^2-x^2\right) d x+2 y d y=0\)
  4. D \(\left(y^2+x^2\right) d x+2 y d y=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left(y^2-x^2\right) d x-2 x y d y=0\)

Step-by-step Solution

Detailed explanation

\((x-a)^2 + y^2 = a^2 \) \(x^2 + y^2 - 2ax = 0 \) \(2x + 2y \frac{dy}{dx} - 2a = 0 \) \(a = x + y \frac{dy}{dx} \) \(x^2 + y^2 - 2x \left(x + y \frac{dy}{dx}\right) = 0 \) \(x^2 + y^2 - 2x^2 - 2xy \frac{dy}{dx} = 0 \) \(y^2 - x^2 - 2xy \frac{dy}{dx} = 0 \)…