$$x^{2}y+2xy^{2}-2x^{2}y+5xy^{2}=7$$
$x=-\frac{\sqrt{49y^{4}-28y}}{2y}+\frac{7y}{2}$
$x=\frac{\sqrt{49y^{4}-28y}}{2y}+\frac{7y}{2}\text{, }y\neq 0$
$y=\frac{\sqrt{x^{4}+196x}}{14x}+\frac{x}{14}$
$y=-\frac{\sqrt{x^{4}+196x}}{14x}+\frac{x}{14}\text{, }x\neq 0$
$x=-\frac{\sqrt{49y^{4}-28y}}{2y}+\frac{7y}{2}$
$x=\frac{\sqrt{49y^{4}-28y}}{2y}+\frac{7y}{2}\text{, }y<0\text{ or }y\geq \frac{\sqrt[3]{4}\times 7^{\frac{2}{3}}}{7}$
$y=\frac{\sqrt{x^{4}+196x}}{14x}+\frac{x}{14}$
$y=-\frac{\sqrt{x^{4}+196x}}{14x}+\frac{x}{14}\text{, }x>0\text{ or }x\leq -\sqrt[3]{196}$