4.311   ODE No. 1311

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

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

Mathematica: cpu = 0.134517 (sec), leaf count = 63 $$\left\{\{y(x)\to c_2{G}_{2,2}^{2,0}(-x^2|\begin{array}{c}\frac{1-v}{2},\frac{v+2}{2}\\ 0,0\end{array})+c_1{}_2{F}_1(\frac{v}{2}+\frac{1}{2},-\frac{v}{2};1;-x^2)\}\right\}$$

Maple: cpu = 0.109 (sec), leaf count = 52 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(-\frac{v}{2},\frac{1}{2}+\frac{v}{2};\frac{1}{2};x^2+1)+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x^2+1}{}_2\text{F}{}_1(1+\frac{v}{2},\frac{1}{2}-\frac{v}{2};\frac{3}{2};x^2+1)\}$$