$\quad(\log x)^x$

$x^{\log x}$

$(\sqrt{x})^{\log x}$

$e^{\sqrt{x} \log x}$

$y=x-4-2 \mathrm{e}^x$

$y=4-x-2 \mathrm{e}^x$

$y=4+x-2 \mathrm{e}^x$

$y=4-x+2 \mathrm{e}^x$

$y(1+x)=x+\mathrm{ce}^x$, where c is the constant of integration

$\quad y(1+x)=\mathrm{ce}^x$, where c is the constant of integration

$y(1-x)=x-\mathrm{ce}^x$, where c is the constant of integration

$y(1+x)=x$, where c is the constant of integration

$x \frac{\mathrm{~d} y}{\mathrm{~d} x}-2 y=0$

$\frac{\mathrm{d} y}{\mathrm{~d} x}+x y=0$

$\quad x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=0$

$x^2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=0$