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JEE Main20249 Apr 2024Morning ShiftMathematicsDifferential EquationsActual

The solution curve, of the differential equation 2 y d y ~d x +3=5 d y ~d x , passing through the point (0,1) is a conic, whose vertex lies on the line:

Options

  1. A2 x+3 y=9
  2. B2 x+3 y=-9
  3. C2 x+3 y=-6
  4. D2 x+3 y=6

Correct answer

A. 2 x+3 y=9

Step-by-step solution

aligned & (2 y-5) d y d x =-3 & (2 y-5) d y=-3 d x & 2 y^2 2 -5 y=-3 x+ aligned Curve passes through (0,1) =-4 Curve will be (y- 5 2 )^2=-3 (x- 3 4 ) Vertex of parabola will be ( 3 4 , 5 2 ) 2 x+3 y=9

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