9.3   ODE No. 1839

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

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

Mathematica: cpu = 0.030004 (sec), leaf count = 25 $$\text{DSolve}[y^{(3)}(x)-y(x)y^{″}(x)+y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.655 (sec), leaf count = 127 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)=(6\mathit{\_}\mathit{f}-1){\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^3+\frac{(7\mathit{\_}\mathit{f}-1){\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^2}{\mathit{\_}\mathit{f}}+\frac{\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)}{\mathit{\_}\mathit{f}}\},\{\mathit{\_}\mathit{f}=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{{\left(y\left(x\right)\right)}^2},\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)=-{\left(y\left(x\right)\right)}^2{(-\frac{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}+2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right))}^{-1}\},\{x=\int \frac{\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)}{\mathit{\_}\mathit{f}{\mathrm{e}}^{\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}}}\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}}\}])\}$$