2.1356   ODE No. 1356

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

$$y^{″}(x)=-\frac{y(x)(-n^2-v(v+1)x^2)}{x^2(x^2+1)}-\frac{(2x^2+1)y^{\prime }(x)}{x(x^2+1)}$$ ✓ Mathematica : cpu = 0.228603 (sec), leaf count = 90

$$\left\{\{y(x)\to c_1{x}^{-n}{}_2{F}_1(-\frac{n}{2}-\frac{v}{2},-\frac{n}{2}+\frac{v}{2}+\frac{1}{2};1-n;-x^2)+c_2{x}^n{}_2{F}_1(\frac{n}{2}-\frac{v}{2},\frac{n}{2}+\frac{v}{2}+\frac{1}{2};n+1;-x^2)\}\right\}$$ ✓ Maple : cpu = 0.456 (sec), leaf count = 29

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