The equation of the curve through the point `(1,0)`, whose slope is `(y-1)/(x^2+x)`

Options

A. `2x+(y-1)(x+1)=0`
B. `2x-(y-1)(x+1)=0`
C. `2x+(y-1)(x-1)=0`
D. None of these

Answer

a

Explanation

Given , `(dy)/(dx) = (y-1)/(x^(2) +x) `
On itegrating both sides , we get
` rArr int (1/x - 1/(x+1)) dx = int 1/(y-1) dy`
` rArr log x - log (x+1) = log (y-1) + log C`
` rArr x/(x+1) = (y-1)C`
Since , this curve passes through (1,0)
` :. C = -1/2`
` :. "From eq. " (i) , 2x + (y-1) (x+1) =0`