9.17   ODE No. 1853

$$\boxed{{\displaystyle 9{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)}^2\frac{{\mathrm{d}}^5}{\mathrm{d}{x}^5}y\left(x\right)-45\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)\right)\mathit{d}\mathit{4}\mathit{y}\left(x\right)+40\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.074009 (sec), leaf count = 41 $$\text{DSolve}[40y^{(3)}(x{)}^3+9y^{(5)}(x)y^{″}(x{)}^2-45y^{(4)}(x)y^{(3)}(x)y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.515 (sec), leaf count = 110 $$\{y\left(x\right)=\int \int \mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-20\ln \left(\mathit{\_}\mathit{f}\right)+{\int }^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{k}({\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(81{\mathit{\_}\mathit{k}}^2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+20{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln ({\mathrm{e}}^{\mathit{\_}\mathit{Z}}+27)-40{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(2\right)-20{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(5\right)+162\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-20\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2187{\mathit{\_}\mathit{k}}^2+540\ln ({\mathrm{e}}^{\mathit{\_}\mathit{Z}}+27)-1080\ln \left(2\right)-540\ln \left(5\right)+4374\mathit{\_}\mathit{C}\mathit{1}-540\mathit{\_}\mathit{Z}-540)}+27)d\mathit{\_}\mathit{k}+20\mathit{\_}\mathit{C}\mathit{2})\right)}^{-1}d\mathit{\_}\mathit{f}+x+\mathit{\_}\mathit{C}\mathit{3})\mathrm{d}x\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{4}x+\mathit{\_}\mathit{C}\mathit{5}\}$$