Solve (1-x^2)y_{2}+2xy_{1}+y=0

$$( 1 - x ^ { 2 } ) y _ { 2 } + 2 x y _ { 1 } + y = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{yy_{2}+y_{1}^{2}+y_{2}^{2}}-y_{1}}{y_{2}}\text{; }x=\frac{\sqrt{yy_{2}+y_{1}^{2}+y_{2}^{2}}+y_{1}}{y_{2}}\text{, }&y_{2}\neq 0\\x=-\frac{y}{2y_{1}}\text{, }&y_{2}=0\text{ and }y_{1}\neq 0\\x\in \mathrm{C}\text{, }&y_{2}=0\text{ and }y_{1}=0\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{yy_{2}+y_{1}^{2}+y_{2}^{2}}-y_{1}}{y_{2}}\text{; }x=\frac{\sqrt{yy_{2}+y_{1}^{2}+y_{2}^{2}}+y_{1}}{y_{2}}\text{, }&y_{2}\neq 0\text{ and }\left(y_{2}\geq \frac{\sqrt{y^{2}-4y_{1}^{2}}-y}{2}\text{ or }y_{2}\leq \frac{-\sqrt{y^{2}-4y_{1}^{2}}-y}{2}\text{ or }|y_{1}|\geq \frac{|y|}{2}\right)\\x=-\frac{y}{2y_{1}}\text{, }&y_{2}=0\text{ and }y_{1}\neq 0\\x\in \mathrm{R}\text{, }&y_{2}=0\text{ and }y_{1}=0\text{ and }y=0\end{matrix}\right.$$

Solve for y

$$y=y_{2}x^{2}-2xy_{1}-y_{2}$$