4.291   ODE No. 1291

$$\boxed{{\displaystyle 48x(x-1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(152x-40)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+53y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.078010 (sec), leaf count = 92 $$\left\{\{y(x)\to c_1{}_2{F}_1(\frac{13}{12}-\frac{\sqrt{\frac{5}{2}}}{6},\frac{13}{12}+\frac{\sqrt{\frac{5}{2}}}{6};\frac{5}{6};x)+\sqrt[6]{-1}{c}_2\sqrt[6]{x}{}_2{F}_1(\frac{5}{4}-\frac{\sqrt{\frac{5}{2}}}{6},\frac{5}{4}+\frac{\sqrt{\frac{5}{2}}}{6};\frac{7}{6};x)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 62 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(\frac{13}{12}-\frac{\sqrt{2}\sqrt{5}}{12},\frac{13}{12}+\frac{\sqrt{2}\sqrt{5}}{12};\frac{5}{6};x)+\mathit{\_}\mathit{C}\mathit{2}\sqrt[6]{x}{}_2\text{F}{}_1(\frac{5}{4}-\frac{\sqrt{2}\sqrt{5}}{12},\frac{5}{4}+\frac{\sqrt{2}\sqrt{5}}{12};\frac{7}{6};x)\}$$