2.1313   ODE No. 1313

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

$$x(-(v-n))(n+v+1)y(x)+(2(n+1)x^2+2n+1)y^{\prime }(x)+x(x^2+1)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.200394 (sec), leaf count = 87

$$\left\{\{y(x)\to c_1{}_2{F}_1(\frac{n}{2}-\frac{v}{2},\frac{n}{2}+\frac{v}{2}+\frac{1}{2};n+1;-x^2)+c_2{x}^{-2n}{}_2{F}_1(-\frac{n}{2}-\frac{v}{2},-\frac{n}{2}+\frac{v}{2}+\frac{1}{2};1-n;-x^2)\}\right\}$$

✓ Maple : cpu = 0.092 (sec), leaf count = 39

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-n}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(v,n,\sqrt{x^2+1})+\mathit{\_}\mathit{C}\mathit{2}{x}^{-n}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(v,n,\sqrt{x^2+1})\}$$