Solve y=xyyyyyyyyy(2*x^2)

$$y=xyyyyyyyyy(2 \times { x }^{ 2 } )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2^{\frac{2}{3}}e^{\frac{2\pi i}{3}}y^{-\frac{8}{3}}}{2}\text{; }x=\frac{2^{\frac{2}{3}}y^{-\frac{8}{3}}}{2}\text{; }x=\frac{2^{\frac{2}{3}}e^{\frac{4\pi i}{3}}y^{-\frac{8}{3}}}{2}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in 2^{\frac{3}{8}}\left(\frac{1}{2}+\frac{1}{2}i\right)x^{-\frac{3}{8}},\frac{2^{\frac{7}{8}}x^{-\frac{3}{8}}}{2},\frac{2^{\frac{7}{8}}ix^{-\frac{3}{8}}}{2},2^{\frac{3}{8}}\left(-\frac{1}{2}+\frac{1}{2}i\right)x^{-\frac{3}{8}},-\frac{2^{\frac{7}{8}}x^{-\frac{3}{8}}}{2},2^{\frac{3}{8}}\left(-\frac{1}{2}-\frac{1}{2}i\right)x^{-\frac{3}{8}},-\frac{2^{\frac{7}{8}}ix^{-\frac{3}{8}}}{2},2^{\frac{3}{8}}\left(\frac{1}{2}-\frac{1}{2}i\right)x^{-\frac{3}{8}}\text{, }&x\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2^{\frac{2}{3}}}{2y^{\frac{8}{3}}}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{2^{\frac{7}{8}}}{2x^{\frac{3}{8}}}\text{; }y=-\frac{2^{\frac{7}{8}}}{2x^{\frac{3}{8}}}\text{, }&x>0\end{matrix}\right.$$