2.1850   ODE No. 1850

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

$$y^{(3)}(x)y^{\prime }(x{)}^3+y^{(4)}(x)y^{\prime }(x)-y^{(3)}(x)y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.0960456 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x]^3*Derivative[3][y][x] - Derivative[2][y][x]*Derivative[3][y][x] + Derivative[1][y][x]*Derivative[4][y][x] == 0, y[x], x]

✓ Maple : cpu = 1.661 (sec), leaf count = 164

$$\{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)=\frac{\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)(12{\left(\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\right)}^2{\mathit{\_}\mathit{h}}^2+3\mathit{\_}\mathit{h}{\left(\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\right)}^2+10\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)\mathit{\_}\mathit{h}+\mathit{\_}\mathit{j}\left(\mathit{\_}\mathit{h}\right)+1)}{\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)=\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^3\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)}{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-3{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)}^2}\},\{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}\}])\}$$