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MHT CET202123 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The differential equation of the family of parabolas with focus at the origin and the X - axis as axis, is

Options

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

Correct answer

A. -y ( d y d x )^2=2 x d y d x -y

Step-by-step solution

Equation of parabola is y^2=4 a(x+a) 2 y d y d x =4 a a= y d y d x 2 Substituting value of ' a ', we get aligned & y^2=4 ( y d y d x 2 ) [x+ ( y d y d x 2 ) ]= (2 y d y d x ) ( 2 x+y d y d x 2 ) & 2 y^2= (2 y d y d x ) (2 x+y d y d x )=4 x y d y d x +2 y^2 ( d y d x )^2 & y=2 x d y d x +y ( d y d x )^2 aligned

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