Find the equation of the curve whose slope is `(y-1)/(x^(2)+x)` and which passes through the point (1,0).

Options

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

Answer

A

Explanation

Slope `=(dy)/(dx)=(y-1)/x^(2)+x`
or `(dy)/(y-1)=(dx)/(x^(2)+x)`
or `int1/(y-1)dy=int(1/x-1/(x+1))dx+C` or `((y-1)(x+1))/x=k`
Putting `x=1, y=0`, we get `k=-2`.
The equation is `(y-1)(x+1)+2x=0`