7.9   ODE No. 1582

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^5}{\mathrm{d}{x}^5}y\left(x\right)+a{x}^{\nu }\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+a\nu x^{\nu -1}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.337543 (sec), leaf count = 787 $$\left\{\{y(x)\to c_5{(\frac{4}{\nu }+1)}^{-\frac{16}{\nu +4}}{\nu }^{-\frac{16}{\nu +4}}{a}^{\frac{4}{\nu +4}}{\left(x^{\nu }\right)}^{\frac{4(\frac{4}{\nu }+1)}{\nu +4}}{}_1{F}_4(\frac{4}{\nu (1+\frac{4}{\nu })}+\frac{1}{1+\frac{4}{\nu }};1+\frac{1}{(1+\frac{4}{\nu })\nu },1+\frac{2}{(1+\frac{4}{\nu })\nu },1+\frac{3}{(1+\frac{4}{\nu })\nu },1+\frac{4}{(1+\frac{4}{\nu })\nu };-\frac{a{\left(x^{\nu }\right)}^{1+\frac{4}{\nu }}}{{(1+\frac{4}{\nu })}^4{\nu }^4})+c_4{(\frac{4}{\nu }+1)}^{-\frac{12}{\nu +4}}{\nu }^{-\frac{12}{\nu +4}}{a}^{\frac{3}{\nu +4}}{\left(x^{\nu }\right)}^{\frac{3(\frac{4}{\nu }+1)}{\nu +4}}{}_1{F}_4(\frac{3}{\nu (1+\frac{4}{\nu })}+\frac{1}{1+\frac{4}{\nu }};1-\frac{1}{(1+\frac{4}{\nu })\nu },1+\frac{1}{(1+\frac{4}{\nu })\nu },1+\frac{2}{(1+\frac{4}{\nu })\nu },1+\frac{3}{(1+\frac{4}{\nu })\nu };-\frac{a{\left(x^{\nu }\right)}^{1+\frac{4}{\nu }}}{{(1+\frac{4}{\nu })}^4{\nu }^4})+c_3{(\frac{4}{\nu }+1)}^{-\frac{8}{\nu +4}}{\nu }^{-\frac{8}{\nu +4}}{a}^{\frac{2}{\nu +4}}{\left(x^{\nu }\right)}^{\frac{2(\frac{4}{\nu }+1)}{\nu +4}}{}_1{F}_4(\frac{2}{\nu (1+\frac{4}{\nu })}+\frac{1}{1+\frac{4}{\nu }};1-\frac{2}{(1+\frac{4}{\nu })\nu },1-\frac{1}{(1+\frac{4}{\nu })\nu },1+\frac{1}{(1+\frac{4}{\nu })\nu },1+\frac{2}{(1+\frac{4}{\nu })\nu };-\frac{a{\left(x^{\nu }\right)}^{1+\frac{4}{\nu }}}{{(1+\frac{4}{\nu })}^4{\nu }^4})+c_2{(\frac{4}{\nu }+1)}^{-\frac{4}{\nu +4}}{\nu }^{-\frac{4}{\nu +4}}{a}^{\frac{1}{\nu +4}}{\left(x^{\nu }\right)}^{\frac{\frac{4}{\nu }+1}{\nu +4}}{}_1{F}_4(\frac{1}{\nu (1+\frac{4}{\nu })}+\frac{1}{1+\frac{4}{\nu }};1-\frac{3}{(1+\frac{4}{\nu })\nu },1-\frac{2}{(1+\frac{4}{\nu })\nu },1-\frac{1}{(1+\frac{4}{\nu })\nu },1+\frac{1}{(1+\frac{4}{\nu })\nu };-\frac{a{\left(x^{\nu }\right)}^{1+\frac{4}{\nu }}}{{(1+\frac{4}{\nu })}^4{\nu }^4})+c_1{}_1{F}_4(\frac{1}{1+\frac{4}{\nu }};1-\frac{4}{(1+\frac{4}{\nu })\nu },1-\frac{3}{(1+\frac{4}{\nu })\nu },1-\frac{2}{(1+\frac{4}{\nu })\nu },1-\frac{1}{(1+\frac{4}{\nu })\nu };-\frac{a{\left(x^{\nu }\right)}^{1+\frac{4}{\nu }}}{{(1+\frac{4}{\nu })}^4{\nu }^4})\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 41 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^5}{\mathrm{d}{x}^5}\mathit{\_}\mathit{Y}\left(x\right)+a{x}^{\nu }\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+a\nu x^{\nu -1}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$