Lutasin ang y=x^2+y^2x/2

$$y = x ^ { 2 } + \frac { y ^ { 2 } x } { 2 }$$

I-solve ang x (complex solution)

$$x=\frac{-\sqrt{y^{4}+16y}-y^{2}}{4}$$

$$x=\frac{\sqrt{y^{4}+16y}-y^{2}}{4}$$

I-solve ang y (complex solution)

$$\left\{\begin{matrix}y=-\frac{\sqrt{1-2x^{3}}-1}{x}\text{; }y=\frac{\sqrt{1-2x^{3}}+1}{x}\text{, }&x\neq 0\\y=0\text{, }&x=0\end{matrix}\right.$$

I-solve ang x

$$x=\frac{-\sqrt{y^{4}+16y}-y^{2}}{4}$$

$$x=\frac{\sqrt{y^{4}+16y}-y^{2}}{4}\text{, }y\leq -2^{\frac{4}{3}}\text{ or }y\geq 0$$

I-solve ang y

$$\left\{\begin{matrix}y=-\frac{\sqrt{1-2x^{3}}-1}{x}\text{; }y=\frac{\sqrt{1-2x^{3}}+1}{x}\text{, }&x\neq 0\text{ and }x\leq \frac{2^{\frac{2}{3}}}{2}\\y=0\text{, }&x=0\end{matrix}\right.$$