2.1233   ODE No. 1233

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

$$\frac{nx{Q}_n(x)-n{Q}_{n-1}(x)}{x^2-1}-n(n+1)y(x)+(x^2-1)y^{″}(x)=0$$ ✗ Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 0.131 (sec), leaf count = 418

$$\{y\left(x\right)=(-x^2+1){}_2\text{F}{}_1(\frac{n}{2}+1,-\frac{n}{2}+\frac{1}{2};\frac{1}{2};x^2)\mathit{\_}\mathit{C}\mathit{2}+(-x^3+x){}_2\text{F}{}_1(1-\frac{n}{2},\frac{n}{2}+\frac{3}{2};\frac{3}{2};x^2)\mathit{\_}\mathit{C}\mathit{1}-3(n+1)(x-1)(1+x)(-{}_2\text{F}{}_1(1-n/2,n/2+3/2;3/2;x^2)\int 1/3\frac{{}_2\text{F}{}_1(n/2+1,-n/2+1/2;1/2;x^2)(x\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(n,x)-\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(n+1,x))}{{(1+x)}^3{(x-1)}^3(({}_2\text{F}{}_1(n/2+1,-n/2+1/2;1/2;x^2)+(n^2+n-2)x^2{}_2\text{F}{}_1(2+n/2,3/2-n/2;3/2;x^2)){}_2\text{F}{}_1(1-n/2,n/2+3/2;3/2;x^2)-1/3{}_2\text{F}{}_1(n/2+1,-n/2+1/2;1/2;x^2){}_2\text{F}{}_1(2-n/2,5/2+n/2;5/2;x^2)x^2(n+3)(n-2))}\mathrm{d}xx+\int 1/3\frac{{}_2\text{F}{}_1(1-n/2,n/2+3/2;3/2;x^2)x(x\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(n,x)-\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(n+1,x))}{{(1+x)}^3{(x-1)}^3(({}_2\text{F}{}_1(n/2+1,-n/2+1/2;1/2;x^2)+(n^2+n-2)x^2{}_2\text{F}{}_1(2+n/2,3/2-n/2;3/2;x^2)){}_2\text{F}{}_1(1-n/2,n/2+3/2;3/2;x^2)-1/3{}_2\text{F}{}_1(n/2+1,-n/2+1/2;1/2;x^2){}_2\text{F}{}_1(2-n/2,5/2+n/2;5/2;x^2)x^2(n+3)(n-2))}\mathrm{d}x{}_2\text{F}{}_1(n/2+1,-n/2+1/2;1/2;x^2))\}$$