2.1839   ODE No. 1839

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

$$y^{(3)}(x)-y(x)y^{″}(x)+y^{\prime }(x{)}^2=0$$ ✗ Mathematica : cpu = 0.0296948 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 1.214 (sec), leaf count = 125

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