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JEE Main20208 Jan 2020Evening ShiftMathematicsDifferential EquationsActual

The differential equation of the family of curves, x 2 = 4 b y + b , b ∈ R , is.

Options

  1. Ax y ' 2 = x + 2 y y '
  2. Bx y ' 2 = 2 y y ' - x
  3. Cx y ' ' = y '
  4. Dx y ' 2 = x - 2 y y '

Correct answer

A. x y ' 2 = x + 2 y y '

Step-by-step solution

x 2 = 4 b y + b Differentiate both sides, 2 x = 4 b y '   ⇒ b = x 2 y ' So, the differential equation is x 2 = 2 x y ' y + x y ' 2 ⟹ x d y d x 2 = 2 y d y d x + x ⇒ x y ' 2 = x + 2 y y '

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