2.1798   ODE No. 1798

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

$$x^{3}y(x{)}^2{y}^{″}(x)+(y(x)+x){(x{y}^{\prime }(x)-y(x))}^3=0$$ ✗ Mathematica : cpu = 38.1617 (sec), leaf count = 0 , could not solve

DSolve[(x + y[x])*(-y[x] + x*Derivative[1][y][x])^3 + x^3*y[x]^2*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.522 (sec), leaf count = 166

$$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}1(i\sqrt{3}{\mathit{Y}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{C}\mathit{1}\sqrt{\mathit{\_}\mathit{f}}+i\sqrt{3}{\mathit{J}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\sqrt{\mathit{\_}\mathit{f}}+{\mathit{Y}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{C}\mathit{1}\sqrt{\mathit{\_}\mathit{f}}-2\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_{i\sqrt{3}+1}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{f}+{\mathit{J}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\sqrt{\mathit{\_}\mathit{f}}-2{\mathit{J}}_{i\sqrt{3}+1}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{f}){\mathit{\_}\mathit{f}}^{-\frac{3}{2}}{({\mathit{Y}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{J}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right))}^{-1}d\mathit{\_}\mathit{f}+2\mathit{\_}\mathit{C}\mathit{2})x\}$$