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MHT CET20239 May 2023Morning ShiftMathematicsDifferential EquationsActual

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

Options

  1. Ay₃=1
  2. By₃=-1
  3. Cy₃=0
  4. Dyy₃+y₁=0

Correct answer

C. y₃=0

Step-by-step solution

Parabola whose axes are parallel to Y -axis. Vertex is not (0,0) Equation becomes (x- h )^2=4 ~b (y- k ) Differentiating w.r.t. x , we get 2(x-h)=4 b ( d y d x ) Again differentiating w.r.t. x , we get 2=4 ~b ( d ^2 y ~d x^2 ) Again differentiating w.r.t. x , we get aligned & 0=4 b ( d ^3 y ~d x^3 ) & d ^3 y ~d x^3 =0 & i.e., y₃=0 aligned

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