Solve 2x*y^2-y^3=-x

$$2x \times { y }^{ 2 } - { y }^{ 3 } =-x$$

Solve for x

$$x=\frac{y^{3}}{2y^{2}+1}$$

Steps for Solving Linear Equation

Add x to both sides.

$$2xy^{2}-y^{3}+x=0$$

Add y^{3} to both sides. Anything plus zero gives itself.

$$2xy^{2}+x=y^{3}$$

Combine all terms containing x.

$$\left(2y^{2}+1\right)x=y^{3}$$

Divide both sides by 2y^{2}+1.

$$\frac{\left(2y^{2}+1\right)x}{2y^{2}+1}=\frac{y^{3}}{2y^{2}+1}$$

Dividing by 2y^{2}+1 undoes the multiplication by 2y^{2}+1.

$$x=\frac{y^{3}}{2y^{2}+1}$$

Solve for y

$$y=\frac{2^{\frac{2}{3}}\sqrt[3]{16x^{3}+3|x|\sqrt{96x^{2}+81}+27x}}{6}+\frac{2^{\frac{2}{3}}\sqrt[3]{16x^{3}-3|x|\sqrt{96x^{2}+81}+27x}}{6}+\frac{2x}{3}$$