7.10   ODE No. 1583

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^5}{\mathrm{d}{x}^5}y\left(x\right)+a\frac{{\mathrm{d}}^4}{\mathrm{d}{x}^4}y\left(x\right)-f=0}}$$

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

Mathematica: cpu = 1218.103679 (sec), leaf count = 117 $$\left\{\{y(x)\to (\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3645023}-1)(\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3818055}-1)(\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3863942}-1)(x-1)e^{-a\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3873056}}(\text{Integrate}[e^{aK[1]}f(K[1]),\{K[1],1,\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3873056}\},\text{Assumptions}\to (\mathrm{\Im }(\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3645023})\ne 0\vee 1<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3818055}<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3645023}\vee \text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3645023}<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3818055}<1)\wedge (\mathrm{\Im }(\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3818055})\ne 0\vee 1<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3863942}<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3818055}\vee \text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3818055}<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3863942}<1)\wedge (\mathrm{\Im }(\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3863942})\ne 0\vee 1<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3873056}<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3863942}\vee \text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3863942}<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3873056}<1)\wedge (\mathrm{\Im }(x)\ne 0\vee 1<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3645023}<x\vee x<\text{Integrate}\stackrel{`}{}\mathrm{\$}\mathrm{\$}\text{a}\mathrm{\$}\text{3645023}<1)]+c_1)+c_5{x}^3+c_4{x}^2+c_{3}x+c_2\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 40 $$\{y\left(x\right)=\frac{{\mathrm{e}}^{-ax}\mathit{\_}\mathit{C}\mathit{1}}{a^4}+\frac{f{x}^4}{24a}+\frac{\mathit{\_}\mathit{C}\mathit{2}{x}^3}{6}+\frac{\mathit{\_}\mathit{C}\mathit{3}{x}^2}{2}+\mathit{\_}\mathit{C}\mathit{4}x+\mathit{\_}\mathit{C}\mathit{5}\}$$