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The differential equation of the family of curves y = k 1 x 2 + k 2 is given by (where, k 1 and k 2 are arbitrary constants and y 1 = d y d x , y 2 = d 2 y d x 2 )

Options

  1. Ay 1 = x 2 y 2
  2. By 1 2 = x y 2
  3. Cx y 2 = y 1
  4. Dy 1 y 2 = x

Correct answer

C. x y 2 = y 1

Step-by-step solution

Differentiating with respect to x , we get, d y d x = 2 k 1 x ⇒ y 1 x = 2 k 1 Differentiating again, we get, x ⋅ y 2 - y 1 x 2 = 0 or x y 2 = y 1

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