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MHT CET202124 Sep 2021Evening ShiftMathematicsDifferential EquationsActual

The differential equation of all parabolas whose axis is y-axis, is

Options

  1. Ad^2 y d x^2 - d y d x =0
  2. Bd^2 y d x^2 + d y d x =0
  3. Cx d^2 y d x^2 - d y d x =0
  4. Dd^2 y d x^2 -y=0

Correct answer

C. x d^2 y d x^2 - d y d x =0

Step-by-step solution

Differential Equation of parabolas whose axis is Y axis, is Let the vertex be (0, k ) aligned & x^2=4 b y-4 b k & 2 x=4 b d y d x -0 b= ( x 2 ) 1 ( d y d x ) & 2 x=4 b d y d x -0 b= ( x 2 ) 1 ( d y d x ) aligned Substituting value of b in eq. (1), we get aligned & x^2=4 ( x 2 ) 1 ( d y d x ) (y-k) & x ^2 ( dy dx )=2 x ( y - k ) & x^2 ( d^2 y d x^2 )+ ( d y d x )(2 x)=2 x d y d x +2(y-k) & y - k = x ^2 ( d ^2 y dx ) 2 & aligned Substituting value of ( y - k ) in eq. (1), we get aligned & .x^2=4 ( x 2 ) [ 1 ( d y d x

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