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AP EAMCET201921 Apr 2019Morning ShiftMathematicsDifferential EquationsActual

The differential equation of all parabolas whose axes are parallel to Y -axis is

Options

  1. Ad^3 y d x^3 =0
  2. Bd^2 y d x^2 =0
  3. Cd^2 y d x^2 + d y d x =0
  4. Dy d^2 y d x^2 + ( d y d x )^2=0

Correct answer

A. d^3 y d x^3 =0

Step-by-step solution

Let y=A x^2+B x+C Differentiate w.r.t. x , we get d y d x =2 A x+B Again, differentiate w.r.t. x , we get d^2 y d x^2 =2 A Again, differentiate w.r.t. x , we get d^3 y d x^3 =0 This is required equation.

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