hi!

my equation is:

$\displaystyle xy` = y+\sqrt{x^2-y^2}$

i've divided by x and used $\displaystyle z=\frac{y}{x}$

and got:

$\displaystyle z`x = \sqrt{1-z^2}$

and further:

$\displaystyle \frac{dz}{dx} = \frac{\sqrt{1-z^2}}{x}$

arranged it a little and integrated both parts, eventually got:

$\displaystyle arcsin(z) = ln(x) + c$

where do i go from here?

i want this equation in y because i have condition in y.

can i put back apply $\displaystyle sin$ on both sides of the equation

to get rid of the $\displaystyle arcsin$? is the way i'm going at this correct?