5.8   ODE No. 1456

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+x^{2c-2}\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(c-1)x^{2c-3}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.034004 (sec), leaf count = 183 $$\left\{\{y(x)\to c_1{}_1{F}_2(\frac{1}{2}-\frac{1}{2c};1-\frac{1}{c},1-\frac{1}{2c};-\frac{x^{2c}}{4c^2})+4^{-1/c}{c}_3{c}^{-2/c}{\left(x^{2c}\right)}^{\frac{1}{c}}{}_1{F}_2(\frac{1}{2}+\frac{1}{2c};1+\frac{1}{2c},1+\frac{1}{c};-\frac{x^{2c}}{4c^2})+2^{-1/c}{c}_2{c}^{-1/c}{\left(x^{2c}\right)}^{\frac{1}{2}/c}{}_1{F}_2(\frac{1}{2};1-\frac{1}{2c},1+\frac{1}{2c};-\frac{x^{2c}}{4c^2})\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 74 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x{\left({\mathit{J}}_{\frac{1}{2c}}\left(\frac{x^c}{2c}\right)\right)}^2+\mathit{\_}\mathit{C}\mathit{2}x{\left({\mathit{Y}}_{\frac{1}{2c}}\left(\frac{x^c}{2c}\right)\right)}^2+\mathit{\_}\mathit{C}\mathit{3}x{\mathit{J}}_{\frac{1}{2c}}\left(\frac{x^c}{2c}\right){\mathit{Y}}_{\frac{1}{2c}}\left(\frac{x^c}{2c}\right)\}$$