Solve 3x^5+15y^2=200x^5y^2

$$3 x ^ { 5 } + 15 y ^ { 2 } = 200 x ^ { 5 } y ^ { 2 }$$

Solve for x (complex solution)

$$x=\sqrt[5]{15}e^{\frac{3i\pi }{5}}\left(3-200y^{2}\right)^{-\frac{1}{5}}y^{\frac{2}{5}}$$

$$x=\sqrt[5]{15}e^{\frac{\pi i}{5}}\left(3-200y^{2}\right)^{-\frac{1}{5}}y^{\frac{2}{5}}$$

$$x=-\sqrt[5]{15}\left(3-200y^{2}\right)^{-\frac{1}{5}}y^{\frac{2}{5}}$$

$$x=\sqrt[5]{15}e^{\frac{7i\pi }{5}}\left(3-200y^{2}\right)^{-\frac{1}{5}}y^{\frac{2}{5}}$$

$$x=\sqrt[5]{15}e^{\frac{9i\pi }{5}}\left(3-200y^{2}\right)^{-\frac{1}{5}}y^{\frac{2}{5}}\text{, }y\neq -\frac{\sqrt{6}}{20}\text{ and }y\neq \frac{\sqrt{6}}{20}$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{15}i\left(3-40x^{5}\right)^{-\frac{1}{2}}x^{\frac{5}{2}}}{5}$$

$$y=\frac{\sqrt{15}i\left(3-40x^{5}\right)^{-\frac{1}{2}}x^{\frac{5}{2}}}{5}\text{, }x\neq \frac{40^{\frac{4}{5}}\sqrt[5]{3}e^{\frac{2\pi i}{5}}}{40}\text{ and }x\neq \frac{40^{\frac{4}{5}}\sqrt[5]{3}}{40}\text{ and }x\neq \frac{40^{\frac{4}{5}}\sqrt[5]{3}e^{\frac{8\pi i}{5}}}{40}\text{ and }x\neq \frac{40^{\frac{4}{5}}\sqrt[5]{3}e^{\frac{6\pi i}{5}}}{40}\text{ and }x\neq \frac{40^{\frac{4}{5}}\sqrt[5]{3}e^{\frac{4\pi i}{5}}}{40}$$

Solve for x

$$x=-\sqrt[5]{\frac{15}{3-200y^{2}}}y^{\frac{2}{5}}$$

$$|y|\neq \frac{\sqrt{6}}{20}$$

Solve for y

$$y=\frac{\sqrt{-\frac{15x^{5}}{3-40x^{5}}}}{5}$$

$$y=-\frac{\sqrt{-\frac{15x^{5}}{3-40x^{5}}}}{5}\text{, }x\leq 0\text{ or }x>\frac{40^{\frac{4}{5}}\sqrt[5]{3}}{40}$$