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MHT CET2017MathematicsDifferential Equations

The differential equation of all parabolas whose axis is y - a x i s is

Options

  1. Ax d 2 y d x 2 - d y d x = 0
  2. Bx d 2 y d x 2 + d y d x = 0
  3. Cd 2 y d x 2 - y = 0
  4. Dd 2 y d x 2 - d y d x = 0

Correct answer

A. x d 2 y d x 2 - d y d x = 0

Step-by-step solution

Axis = y axis Vertex is (0, k) Equation of parabola is x - 0 2 = 4 a y - k x 2 = 4 a y - 4 a k Differentiate w.r.t x, 2 x = 4 a d y d x ⇒ x = 2 a d y d x ∴ 1 2 a = 1 x d y d x Differentiate w.r.t x, d d x 1 x ⋅ d y d x = d d x 1 2 a ⇒ 1 x ⋅ d 2 y d x 2 + d y d x - 1 x 2 = 0 ⇒ ∴ x d 2 y d x 2 - d y d x = 0

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