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AP EAMCET202420 May 2024Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation (y^2+x+1 ) d y=(y+1) d x is

Options

  1. Ax+2+(y+1) (y+1)^2=y+c
  2. Bx+2+ (y+1)^2= y y+1 +c
  3. Cx y+1 = (y+1)^2+y+c
  4. Dx+2 y+1 + (y+1)^2=y+c

Correct answer

D. x+2 y+1 + (y+1)^2=y+c

Step-by-step solution

d x d y = y^2+x+1 y+1 d x d y - x y+1 = y^2+1 y+1 If =e^ - 1 y+1 d y = 1 y+1 x y+1 = y^2+1 (y+1)^2 d y= (1- 2 y (y+1)^2 ) d y x y+1 =y-2 |y+1|- 2 y+1 +c x+2 y+1 +2 (y+1)=y+c

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