An equation of the curve satisfying `x dy - y dx = sqrt(x^(2)-y^(2))dx` and y(1) = 0 is

Options

A. `y = x^(2) log |sin x|`
B. `y = x sin (log|x|)`
C. `y^(2)=x(x-1)^(2)`
D. `y = 2x^(2)(x - 1)`

Answer

B

Explanation

The equation can be written as
`x^(2)(x dy-y dx)/(x^(2))=x sqrt(1-(y//x)^(2))dx`
`rArr" "(d(y//x))/(sqrt(1-(y//x)^(2)))=(dx)/(x)`
`rArr" "sin^(-1) y//x = log |x| + c`
Since y(1) = 0, c = 0.
Hence y = x sin (log|x|)