4.258   ODE No. 1258

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

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

Mathematica: cpu = 0.162021 (sec), leaf count = 146 $$\left\{\{y(x)\to (-1{)}^{b+1}{c}_2{x}^{b+1}{}_2{F}_1(\frac{a}{2}+b-\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{1}{2},\frac{a}{2}+b+\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{1}{2};b+2;x)+c_1{}_2{F}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{1}{2},\frac{a}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{1}{2};-b;x)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 110 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(-\frac{1}{2}-\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{a}{2},-\frac{1}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{a}{2};-b;x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{b+1}{}_2\text{F}{}_1(\frac{1}{2}-\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{a}{2}+b,\frac{1}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{a}{2}+b;b+2;x)\}$$