9.14   ODE No. 1850

$$\boxed{{\displaystyle \left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\mathit{d}\mathit{4}\mathit{y}\left(x\right)-\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.083511 (sec), leaf count = 37 $$\text{DSolve}[y^{(4)}(x)y^{\prime }(x)-y^{(3)}(x)y^{″}(x)+y^{(3)}(x)y^{\prime }(x{)}^3=0,y(x),x]$$

Maple: cpu = 1.092 (sec), leaf count = 165 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\int \frac{\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)}{{\mathrm{e}}^{\int \mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\mathrm{d}\mathit{\_}\mathit{h}+\mathit{\_}\mathit{C}\mathit{2}}\mathit{\_}\mathit{h}}\mathrm{d}\mathit{\_}\mathit{h}+\mathit{\_}\mathit{C}\mathit{3},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{h}}\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)=(12\mathit{\_}\mathit{h}+3){\left(\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\right)}^3+\frac{(10\mathit{\_}\mathit{h}+1){\left(\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\right)}^2}{\mathit{\_}\mathit{h}}+\frac{\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)}{\mathit{\_}\mathit{h}}\},\{\mathit{\_}\mathit{h}=\frac{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}{{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^3},\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)=-{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^3{(-\frac{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)}{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}+3\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right))}^{-1}\},\{x=\int \frac{\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)}{\mathit{\_}\mathit{h}{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\mathrm{d}\mathit{\_}\mathit{h}+\mathit{\_}\mathit{C}\mathit{2}}\right)}^2}\mathrm{d}\mathit{\_}\mathit{h}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\int \frac{\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)}{{\mathrm{e}}^{\int \mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\mathrm{d}\mathit{\_}\mathit{h}+\mathit{\_}\mathit{C}\mathit{2}}\mathit{\_}\mathit{h}}\mathrm{d}\mathit{\_}\mathit{h}+\mathit{\_}\mathit{C}\mathit{3}\}])\}$$