8.92   ODE No. 1682

$$\boxed{{\displaystyle x^3(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^3)+12xy\left(x\right)+24=0}}$$

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

Mathematica: cpu = 22.595369 (sec), leaf count = 35 $$\text{DSolve}[x^3(y^{″}(x)+y(x)y^{\prime }(x)-y(x{)}^3)+12xy(x)+24=0,y(x),x]$$

Maple: cpu = 1.186 (sec), leaf count = 102 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(-{\mathit{\_}\mathit{a}}^3-{\mathit{\_}\mathit{a}}^2+14\mathit{\_}\mathit{a}+24){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(-\mathit{\_}\mathit{a}+3){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=xy\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{1}{x(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right))}\},\{x={\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^{-1},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$