3.759   ODE No. 759

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{-\frac{i}{243}(54i{x}^2+81{\left(y\left(x\right)\right)}^4+18x^4{\left(y\left(x\right)\right)}^2+x^8)x}{y\left(x\right)}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 40.967202 (sec), leaf count = 46 $$\text{DSolve}[y^{\prime }(x)=-\frac{ix(x^8+18x^{4}y(x{)}^2+54i{x}^2+81y(x{)}^4)}{243y(x)},y(x),x]$$

Maple: cpu = 0.452 (sec), leaf count = 315 $$\{y\left(x\right)=\frac{-\frac{1}{6}-\frac{i}{6}}{x}\sqrt{(1-i)({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))(\mathit{\_}\mathit{C}\mathit{1}(-27-27i-(1-i)x^6){\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+(-27-27i-(1-i)x^6){\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+6x^3\sqrt{6}({\mathit{J}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)))}{({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))}^{-1},y\left(x\right)=\frac{\frac{1}{6}+\frac{i}{6}}{x}\sqrt{(1-i)({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))(\mathit{\_}\mathit{C}\mathit{1}(-27-27i-(1-i)x^6){\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+(-27-27i-(1-i)x^6){\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+6x^3\sqrt{6}({\mathit{J}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)))}{({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))}^{-1}\}$$