2.1311   ODE No. 1311

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

$$-v(v+1)xy(x)+x(x^2+1)y^{″}(x)+(2x^2+1)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.109689 (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 = 0.201 (sec), leaf count = 52

$$\{y\left(x\right)=c_1\mathrm{hypergeom}([-\frac{v}{2},\frac{v}{2}+\frac{1}{2}],\left[\frac{1}{2}\right],x^2+1)+c_2\sqrt{x^2+1}\mathrm{hypergeom}([\frac{v}{2}+1,-\frac{v}{2}+\frac{1}{2}],\left[\frac{3}{2}\right],x^2+1)\}$$