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MHT CET20225 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

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

Options

  1. A2 3
  2. B1 3
  3. C- 1 3
  4. D1

Correct answer

B. 1 3

Step-by-step solution

aligned & 2+ x y+1 d y d x =- x & d y y+1 = - x d x 2+ x & _ e |y+1|=- _ e |2+ x|+ _ e C & _e|y+1|+ _e|2+ x|= _e C & _e|(y+1)(2+ x)|= _e C & (y+1)(2+ x)=C & Putting x=0 and y=1 we get c=4 & (y+1)(2+ x)=4 & aligned Now putting x= 2 we get y= 1 3

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