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MHT CET202410 May 2024Morning ShiftMathematicsDifferential EquationsActual

If x ~d y ~d x -y x=6 x, 0 x 2 , then general solution of the differential equation is

Options

  1. Ay= x+3 x^2+ c , where c is a constant of integration.
  2. By+ x=3 x^2+ c , where c is a constant of integration.
  3. Cy=3 x^2 x+ x , where c is a constant of integration.
  4. Dy x=3 x^2+ c , where c is a constant of integration.

Correct answer

D. y x=3 x^2+ c , where c is a constant of integration.

Step-by-step solution

aligned & x ~d y ~d x -y x=6 x & ~d y ~d x -( x) y=6 x x aligned This equation is of the form d y ~d x + p y= Q If = e ^ pdx = e ^ - x d x = e ^ x x = x Solution of given equation is aligned & y x= 6 x x x ~d x+ c & y x= 6 x ~d x+ c & y x=3 x^2+ c aligned

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