2.1261   ODE No. 1261

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

$$y(x)(2lx(-n+p-1)+2lp+m)+2(x(-2l+n+1)-l{x}^2+n+1)y^{\prime }(x)+x(x+2)y^{″}(x)=0$$ ✗ Mathematica : cpu = 2.76288 (sec), leaf count = 0 , DifferentialRoot result

$$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {(-2 unicode {f817} l-2 unicode {f817} n l+2 unicode {f817} p l+2 p l+m) unicode {f818}(unicode {f817})+2 left (-l unicode {f817}^2-2 l unicode {f817}+n unicode {f817}+unicode {f817}+n+1right ) unicode {f818}'(unicode {f817})+unicode {f817} (unicode {f817}+2) unicode {f818}''(unicode {f817})=0,unicode {f818}(1)=c\_1,unicode {f818}'(1)=c\_2right }right )(x)right }right }}$$

✓ Maple : cpu = 0.257 (sec), leaf count = 124

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(4l,n,n,-4pl,\frac{(4n+4p+4)l}{2}-\frac{n^2}{2}+m-n,-\frac{x}{2}){(x+2)}^{-\frac{n}{2}-\frac{1}{2}}{(-\frac{x}{2}-1)}^{\frac{n}{2}+\frac{1}{2}}+\mathit{\_}\mathit{C}\mathit{2}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(4l,-n,n,-4pl,\frac{(4n+4p+4)l}{2}-\frac{n^2}{2}+m-n,-\frac{x}{2}){(x+2)}^{-\frac{n}{2}-\frac{1}{2}}{x}^{-n}{(-\frac{x}{2}-1)}^{\frac{n}{2}+\frac{1}{2}}\}$$