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AP EAMCET202317 May 2023Morning ShiftMathematicsDifferential EquationsActual

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

Options

  1. Aa circle
  2. Ba part of parabola
  3. Ca part of ellipse
  4. Da part of hyperbola

Correct answer

D. a part of hyperbola

Step-by-step solution

(1+y^2 ) dx -x y d y=0 d x x - y 1+y^2 d y=0 Integrating both sides: aligned & x- 1 2 (1+y^2 )= c & x 1+y^2 =c x= [c] 1+y^2 ...(i) & y(1)=0 & 1= [c] 1+0 c=1 aligned From equation (i), x= 1+y^2 x^2=1+y^2 x^2-y^2=1 which represents a hyperbola.

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