2.1285   ODE No. 1285

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

$$((4a+2)x-a)y^{\prime }(x)+(a-1)ay(x)+x(4x-1)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.340803 (sec), leaf count = 119

$$\left\{\{y(x)\to \frac{\sqrt[4]{4x-1}{x}^{\frac{1}{2}-\frac{a}{2}}{e}^{-\sqrt{-(a-1{)}^2}{\tan }^{-1}\left(\sqrt{4x-1}\right)}(4\sqrt{-(a-1{)}^2}{c}_1{e}^{2\sqrt{-(a-1{)}^2}{\tan }^{-1}\left(\sqrt{4x-1}\right)}-c_2)}{2\sqrt{-(a-1{)}^2}\sqrt[4]{1-4x}}\}\right\}$$

✓ Maple : cpu = 0.119 (sec), leaf count = 52

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(\frac{a}{2},\frac{a}{2}-\frac{1}{2};a;4x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{1-a}{}_2\text{F}{}_1(1-\frac{a}{2},-\frac{a}{2}+\frac{1}{2};-a+2;4x)\}$$