The equation of the curve through the point (1,0) which satisfies the differential equatoin `(1+y^(2))dx-xydy=0`, is

Options

A. `x^(2)+y^(2)=4`
B. `x^(2)-y^(2)=1`
C. `2x^(2)+y^(2)=2`
D. None of these

Answer

B

Explanation

Given equation can be rewritten as `(dx)/(x)=(ydy)/(1+y^(2))`
On integrating, we get
`logx=(1)/(2)log(1+y^(2))+logc`
`impliesx=csqrt(1+y^(2))`
but is passes through (1,0). So, we get
`c=1`
`therefore` solution is `x^(2)=y^(2)+1`
`impliesx^(2)-y^(2)=1`