# another 1st order diff. eq.

• Feb 1st 2010, 08:09 AM
vonflex1
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?
• Feb 1st 2010, 08:41 AM
songoku
Hi vonflex

I don't check your work but yes you can apply sin to both sides
• Feb 1st 2010, 09:12 PM
snaes
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.