$$\left. \begin{array} { l } { ( 1 + y ^ { 2 } ) d x + x y d y = 0 } \end{array} \right.$$
$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-\frac{\sqrt{2}i}{2}\text{ or }y=\frac{\sqrt{2}i}{2}\text{ or }d=0\end{matrix}\right.$
$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$
