The equation of a curve passing through `(2,7/2)` and having gradient `1-1/(x^2)` at `(x , y)` is

Options

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

Answer

b

Explanation

We have, `(dy)/(dx) = 1 - 1/(x^(2))`
On integrating both sides , we get
` y = x + 1/x +C`
This passes through `(2,7/2)`
` :. 7/2 = 2+ 1/2 + C rArr C = 1`
Thus, the equation of the curve is
` y = x + 1/x +1 or xy = x^(2) + x +1`