Løs y^3+x^2/y=5+2z(y^2-1)/y

$${ y }^{ 3 } + \frac{ { x }^{ 2 } }{ y } =5+ \frac{ 2z( { y }^{ 2 } -1) }{ y }$$

Løs for x (complex solution)

$$x=-\sqrt{-y^{4}+5y+2zy^{2}-2z}$$

$$x=\sqrt{-y^{4}+5y+2zy^{2}-2z}\text{, }y\neq 0$$

Løs for x

$$x=\sqrt{-y^{4}+5y+2zy^{2}-2z}$$

$$x=-\sqrt{-y^{4}+5y+2zy^{2}-2z}\text{, }\left(y\leq 1\text{ or }z\geq -\frac{y\left(5-y^{3}\right)}{2\left(y^{2}-1\right)}\right)\text{ and }\left(y>-1\text{ or }\left(y\neq -1\text{ and }z\geq -\frac{y\left(5-y^{3}\right)}{2\left(y^{2}-1\right)}\right)\right)\text{ and }\left(y<-1\text{ or }y\geq 1\text{ or }z\leq -\frac{y\left(5-y^{3}\right)}{2\left(y^{2}-1\right)}\right)\text{ and }y\neq 0$$