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AP EAMCET201822 Apr 2018Evening ShiftMathematicsDifferential EquationsActual

The differential equation corresponding to the family of parabolas y^2=4 a(x+a) , where a is the parameter, is

Options

  1. Ay ( d y d x )^2+2 x d y d x +y=0
  2. By ( d y d x )^2-2 x d y d x -y=0
  3. Cy ( d y d x )^2+2 x ( d y d x )-y=0
  4. Dy=2 x d y d x

Correct answer

C. y ( d y d x )^2+2 x ( d y d x )-y=0

Step-by-step solution

Given family of parabola is From Eqs. (i) and (ii), aligned & y^2=4 x ( 1 2 y d y d x )+4 ( 1 2 y d y d x )^2 & y ( d y d x )^2+2 x d y d x -y=0 aligned

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