$5(y-x)+2 \log \left(\frac{y-2}{x-2}\right)=C$

$2(y-x)-5 \log \left(\frac{y-2}{x-2}\right)=C$

$2(y-x)+5 \log \left(\frac{y-2}{x-2}\right)=C$

$5(y-x)-2 \log \left(\frac{y-2}{x-2}\right)=C$

$\left(y^2+x^2\right) d x-2 y d y=0$

$\left(y^2-x^2\right) d x-2 x y d y=0$

$\left(y^2-x^2\right) d x+2 y d y=0$

$\left(y^2+x^2\right) d x+2 y d y=0$

$y-x=c x^2$

$\tan ^{-1}\left(\frac{y}{x}\right)=\log \left(c x \sqrt{x^2+y^2}\right)$

$x+y=c x^2$

$\tan ^{-1}\left(\frac{y}{x}\right)=\log \left(c \sqrt{x^2+y^2}\right)$

$(\cos x+\sin x) y=\sin x+C$

$(\cos x+\sin x) y=\cos x+C$

$(1+\tan x) y=\cos x+C$

$\sec x(\cos x+\sin x) y=\sin x+C$