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MHT CET20239 May 2023Morning ShiftMathematicsDifferential EquationsActual

The particular solution of the differential equation (1+y^2 ) d x-x y ~d y=0 at x=1, y=0 , represents

Options

  1. Acircle
  2. Bpair of straight lines
  3. Chyperbola
  4. Dellipse

Correct answer

C. hyperbola

Step-by-step solution

array ll & (1+y^2 ) d x-x y ~d y=0 & (1+y^2 ) d x=x y ~d y & 1 x ~d x= y ~d y 1+y^2 array Integrating both sides, we get aligned & 1 x ~d x= y 1+y^2 ~d y & x= 1 2 (1+y^2 )+ c aligned At x=1, y=0...[Given] array ll & 0= 1 2 (1+0)+ c & c =0 & x= 1 2 (1+y^2 ) & x^2=1+y^2 & x^2-y^2=1, array Which is a rectangular hyperbola.

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