4.260   ODE No. 1260

$$\boxed{{\displaystyle x(x-1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+((\mathit{a}\mathit{1}+\mathit{b}\mathit{1}+1)x-\mathit{d}\mathit{1})\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+\mathit{a}\mathit{1}\mathit{b}\mathit{1}\mathit{d}\mathit{1}=0}}$$

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

Mathematica: cpu = 0.160020 (sec), leaf count = 65 $$\left\{\{y(x)\to \text{a1}\text{b1}x\mathrm{\Gamma }(\text{d1}+1){}_3{\tilde{F}}_2(1,\text{a1}+\text{b1}+1,1;\text{d1}+1,2;x)-\frac{c_1{x}^{1-\text{d1}}{}_2{F}_1(1-\text{d1},\text{a1}+\text{b1}-\text{d1}+1;2-\text{d1};x)}{\text{d1}-1}+c_2\}\right\}$$

Maple: cpu = 0.296 (sec), leaf count = 76 $$\{y\left(x\right)=\int (-{\left(\mathit{s}\mathit{i}\mathit{g}\mathit{n}\mathit{u}\mathit{m}(x-1)\right)}^{\mathit{a}\mathit{1}+\mathit{b}\mathit{1}-\mathit{d}\mathit{1}}{(-\mathit{s}\mathit{i}\mathit{g}\mathit{n}\mathit{u}\mathit{m}(x-1))}^{-\mathit{a}\mathit{1}-\mathit{b}\mathit{1}+\mathit{d}\mathit{1}}{}_2\text{F}{}_1(\mathit{d}\mathit{1},-\mathit{a}\mathit{1}-\mathit{b}\mathit{1}+\mathit{d}\mathit{1};1+\mathit{d}\mathit{1};x)\mathit{a}\mathit{1}\mathit{b}\mathit{1}+x^{-\mathit{d}\mathit{1}}\mathit{\_}\mathit{C}\mathit{1}){(x-1)}^{-\mathit{a}\mathit{1}-\mathit{b}\mathit{1}-1+\mathit{d}\mathit{1}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2}\}$$