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MHT CET202611 April 2026Morning ShiftMathematicsDifferential EquationsActual

The differential equation representing the family of curves x x + y^3 = 4ax is

Options

  1. Ady dx = y^3 + x^2 x 3xy^2
  2. Bdy dx = y^3 - x^2 x 3xy^2
  3. Cdy dx = y^3 - x^2 x 3xy
  4. Ddy dx = y^3 - x^2 x 3x^2 y

Correct answer

B. dy dx = y^3 - x^2 x 3xy^2

Step-by-step solution

The given equation of the family of curves is x x + y^3 = 4ax . Dividing the entire equation by x , we get: x + y^3 x = 4a Differentiating both sides with respect to x , we obtain: x + 3y^2 dy dx x - y^3 1 x^2 = 0 Multiplying the equation by x^2 gives: x^2 x + 3xy^2 dy dx - y^3 = 0 Rearranging the terms to solve for dy dx : 3xy^2 dy dx = y^3 - x^2 x dy dx = y^3 - x^2 x 3xy^2 Answer: dy dx = y^3 - x^2 x 3xy^2

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