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## Homework Statement

Find the general solution of

y' = [tex] - \frac{x}{y} - \sqrt{(\frac{x}{y})^2 + 1}[/tex]

## Homework Equations

## The Attempt at a Solution

I let y = ux -> y' + xu' + u

xu' + u = - u - [tex]\sqrt{u^2+1}[/tex]

u' = [tex]\frac{-2u - \sqrt{u^2 + 1}}{x}[/tex]

[tex]\frac{du}{-2u - \sqrt{u^2 + 1}} = \frac{dx}{x}[/tex]

now I'm supposed to integrate both sides, just not sure how to find the integral of [tex]\frac{du}{-2u - \sqrt{u^2 + 1}}[/tex]