2.759   ODE No. 759

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

$$y^{\prime }(x)=-\frac{ix(x^8+18x^{4}y(x{)}^2+54i{x}^2+81y(x{)}^4)}{243y(x)}$$ ✗ Mathematica : cpu = 40.7661 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == ((-I/243)*x*((54*I)*x^2 + x^8 + 18*x^4*y[x]^2 + 81*y[x]^4))/y[x], y[x], x]

✓ Maple : cpu = 0.645 (sec), leaf count = 315

$$\{y\left(x\right)=\frac{-\frac{1}{6}-\frac{i}{6}}{x}\sqrt{(1-i)({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))((-27-27i-(1-i)x^6)\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+(-27-27i-(1-i)x^6){\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+6x^3\sqrt{6}({\mathit{J}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)))}{({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))}^{-1},y\left(x\right)=\frac{\frac{1}{6}+\frac{i}{6}}{x}\sqrt{(1-i)({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))((-27-27i-(1-i)x^6)\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+(-27-27i-(1-i)x^6){\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)+6x^3\sqrt{6}({\mathit{J}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{4/3}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)))}{({\mathit{J}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{1}{3}}\left((\frac{2}{27}-\frac{2i}{27})\sqrt{6}{x}^3\right))}^{-1}\}$$