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MHT CET202416 May 2024Morning ShiftMathematicsDifferential EquationsActual

Let y=y(x) be the solution of the differential equation (x x) d y ~d x +y=2 x x(x 1) then y( e ) is equal to

Options

  1. A2
  2. B2 e
  3. Ce
  4. D1

Correct answer

A. 2

Step-by-step solution

aligned & Given, (x x) d y ~d x +y=2 x x & When x=1, y=0 & (x x) d y ~d x +y=2 x x & ~d y ~d x + y x x =2 & I.F. = e ^ 1 x x ~d x = e ^ ( x) = x aligned Solution of the given equation is array ll & y x= 2 x ~d x+ c & y x=2(x x-x)+ c & When x=1, y=0 & 0=-2+ c c =2 & y x=2(x x-x)+2 & y( e )=2( e - e )+2=2 array

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