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MHT CET20227 Aug 2022Evening ShiftMathematicsDifferential EquationsActual

The differential equation x^2(y+1) d x+y^2(x-1) d y=0 has the general solution given by (where C is a constant of integration.)

Options

  1. A(x-1)^2+(y-1)^2+2 [(x+1)(y+1)]=C
  2. B(x-1)^2+(y+1)^2+2 [(x+1)(y-1)]=C
  3. C(x+1)^2+(y+1)^2+2 [(x-1)(y+1)]=C
  4. D(x+1)^2+(y-1)^2+2 [(x-1)(y+1)]=C

Correct answer

D. (x+1)^2+(y-1)^2+2 [(x-1)(y+1)]=C

Step-by-step solution

aligned & x^2(y+1) d x+y^2(x-1) d y=0 & x^2 1-x d x= y^2 y-1 d y & (-x-1+ 1 1+x ) d x= (y-1+ 1 y+1 ) d y & - x^2 2 -x- |1-x+C^1= y^2 2 -y+ | y+1 & C^1=+x+-y+ |1-x|+ |y+1| & 2 C^1=x^2+2 x+y^2-2 y+2 |(1-x)(y+1)| & 2 C^1+2=(x+1)^2+(y-1)^2+2 |(1-x)(y+1)| aligned (x+1)^2+(y-1)^2+2 |(x-1)(y+1)|=C

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