Solve x^2y-x^2+4y=0

$$x ^ { 2 } y - x ^ { 2 } + 4 y = 0$$

Solve for y (complex solution)

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

$$x\neq -2i\text{ and }x\neq 2i$$

Steps for Solving Linear Equation

Add x^{2} to both sides. Anything plus zero gives itself.

$$x^{2}y+4y=x^{2}$$

Combine all terms containing y.

$$\left(x^{2}+4\right)y=x^{2}$$

Divide both sides by x^{2}+4.

$$\frac{\left(x^{2}+4\right)y}{x^{2}+4}=\frac{x^{2}}{x^{2}+4}$$

Dividing by x^{2}+4 undoes the multiplication by x^{2}+4.

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

Solve for y

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

Steps for Solving Linear Equation

Add x^{2} to both sides. Anything plus zero gives itself.

$$x^{2}y+4y=x^{2}$$

Combine all terms containing y.

$$\left(x^{2}+4\right)y=x^{2}$$

Divide both sides by x^{2}+4.

$$\frac{\left(x^{2}+4\right)y}{x^{2}+4}=\frac{x^{2}}{x^{2}+4}$$

Dividing by x^{2}+4 undoes the multiplication by x^{2}+4.

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

Solve for x (complex solution)

$$x=-2i\left(y-1\right)^{-\frac{1}{2}}\sqrt{y}$$

$$x=2i\left(y-1\right)^{-\frac{1}{2}}\sqrt{y}\text{, }y\neq 1$$

Solve for x

$$x=2\sqrt{-\frac{y}{y-1}}$$

$$x=-2\sqrt{-\frac{y}{y-1}}\text{, }y\geq 0\text{ and }y<1$$