# Thread: another 1st order diff. eq.

1. ## another 1st order diff. eq.

hi!

my equation is:

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

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

and got:

$zx = \sqrt{1-z^2}$

and further:

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

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

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

where do i go from here?

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

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

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

2. Hi vonflex

I don't check your work but yes you can apply sin to both sides

3. The same basic rules apply to differential equations. What you do to one side you must do to the other, so yes you are allowed to take the $sin$ of each side.