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COMEDK2015MathematicsDifferential Equations

The differential equation of the family of parabolas y²=4 a x , where a is parameter, is

Options

  1. Ad y d x = y 2 x
  2. Bd y d x =- y 2 x
  3. Cd y d x =- 2 y x
  4. Dd y d x = 2 y x

Correct answer

A. d y d x = y 2 x

Step-by-step solution

Given, equation of parabola is y²=4 a x ...(i) Differentiating E g . (i) w.r.t. x , we get aligned 2 y d y d x &=4 a d y d x &= 2 a y a= y 2 d y d x aligned Substituting the value of a in Eq. (i), we get aligned y² &=4 y 2 d y d x x y² &=2 x y d y d x d y d x = y 2 x aligned

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