6.40   ODE No. 1573

$$\boxed{{\displaystyle ({\mathrm{e}}^x+2x)\mathit{d}\mathit{4}\mathit{y}\left(x\right)+4({\mathrm{e}}^x+2)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+6{\mathrm{e}}^x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+4{\mathrm{e}}^x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right){\mathrm{e}}^x-x^{-5}=0}}$$

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

Mathematica: cpu = 0.054507 (sec), leaf count = 59 $$\text{DSolve}[-\frac{1}{x^5}+(2x+e^x)y^{(4)}(x)+4(e^x+2)y^{(3)}(x)+6e^x{y}^{″}(x)+4e^x{y}^{\prime }(x)+e^{x}y(x)=0,y(x),x]$$

Maple: cpu = 0.016 (sec), leaf count = 65 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{4}}{{\mathrm{e}}^x+2x}+\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^3}{{\mathrm{e}}^x+2x}+\frac{\mathit{\_}\mathit{C}\mathit{2}{x}^2}{{\mathrm{e}}^x+2x}+\frac{\mathit{\_}\mathit{C}\mathit{3}x}{{\mathrm{e}}^x+2x}+\frac{1}{(24{\mathrm{e}}^x+48x)x}\}$$