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MHT CET20242 May 2024Evening ShiftMathematicsDifferential EquationsActual

If (2+ x) d y ~d x +(y+1) x=0 and y(0)=1 , then y ( 2 ) is equal to

Options

  1. A- 2 3
  2. B- 1 3
  3. C4 3
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

array ll & (2+ x) d y ~d x +(y+1) x=0 & 1 y+1 ~d y= - x 2+ x ~d x & Integrating on both sides, we get & (y+1)=- (2+ x)+ c & When x=0, y=1 & c =2 2= 4 & (i) (y+1)=- (2+ x)+ 4 & (y+1)= ( 4 2+ x ) array aligned & y+1= 4 2+ x & y= 4 2+ x -1 & y ( 2 )= 4 3 -1= 1 3 aligned

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