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Manipal MET2017MathematicsDifferential Equations

The solution of the equation (2 y-1) d x-(2 x+3) d y=0 is

Options

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

Correct answer

B. 2 x+3 2 y-1 =c

Step-by-step solution

The given equation is (2 y-1) d x-(2 x+3) d y=0 or it can be rewritten as d x (2 x+3) - d y (2 y-1) =0 On integrating both sides, we get gathered 1 (2 x+3) d x- 1 (2 y-1) d y=0 1 2 (2 x+3)- 1 2 (2 y-1)= 1 2 c ( 2 x+3 2 y-1 )= c 2 x+3 2 y-1 =c gathered

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