4.259   ODE No. 1259

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

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

Mathematica: cpu = 0.142018 (sec), leaf count = 120 $$\left\{\{y(x)\to (-1{)}^{b+1}{c}_2{x}^{b+1}{}_2{F}_1(\frac{a}{2}+b-\frac{1}{2}\sqrt{a^2+4l}+1,\frac{a}{2}+b+\frac{1}{2}\sqrt{a^2+4l}+1;b+2;x)+c_1{}_2{F}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2+4l},\frac{a}{2}+\frac{1}{2}\sqrt{a^2+4l};-b;x)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 92 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2+4l},\frac{a}{2}+\frac{1}{2}\sqrt{a^2+4l};-b;x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{b+1}{}_2\text{F}{}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2+4l}+b+1,\frac{a}{2}+\frac{1}{2}\sqrt{a^2+4l}+b+1;b+2;x)\}$$