8.231   ODE No. 1821

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

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

Mathematica: cpu = 42.477894 (sec), leaf count = 45 $$\text{DSolve}[(x^2+2y(x{)}^2{y}^{\prime }(x))y^{″}(x)+2y(x)y^{\prime }(x{)}^3+3x{y}^{\prime }(x)+y(x)=0,y(x),x]$$

Maple: cpu = 1.529 (sec), leaf count = 54 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+{\mathit{\_}\mathit{a}}^2\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\}$$