The answer for $\displaystyle

x sin (\frac {y}{x})y' = xcos(\frac {y}{x}) + ysin(\frac {y}{x})

$ is given as,

$\displaystyle

xcos(\frac {y}{x}) = c.

$

Where as my answer after simplifying the following step,

$\displaystyle

\frac {dv}{cot(v)} = \frac {dx}{x}

$

was,

$\displaystyle

-cos (\frac {y}{x}) = xc

$

I have tried my best to get the required form but I couldn't. Where does the problem lie?