4.285   ODE No. 1285

$$\boxed{{\displaystyle x(4x-1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+((4a+2)x-a)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+a(a-1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.335543 (sec), leaf count = 134 $$\left\{\{y(x)\to \frac{2c_1\sqrt[4]{4x-1}{x}^{\frac{1}{2}-\frac{a}{2}}{e}^{\sqrt{-(a-1{)}^2}{\tan }^{-1}\left(\sqrt{4x-1}\right)}}{\sqrt[4]{1-4x}}-\frac{c_2\sqrt[4]{4x-1}{x}^{\frac{1}{2}-\frac{a}{2}}{e}^{-\sqrt{-(a-1{)}^2}{\tan }^{-1}\left(\sqrt{4x-1}\right)}}{2\sqrt{-(a-1{)}^2}\sqrt[4]{1-4x}}\}\right\}$$

Maple: cpu = 0.079 (sec), leaf count = 52 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(\frac{a}{2},\frac{a}{2}-\frac{1}{2};a;4x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{1-a}{}_2\text{F}{}_1(1-\frac{a}{2},-\frac{a}{2}+\frac{1}{2};-a+2;4x)\}$$