2.1172   ODE No. 1172

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

$$ay(x)+x^2{y}^{″}(x)+2(x-1)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0551905 (sec), leaf count = 158

$$\left\{\{y(x)\to 2^{\frac{1}{2}(1-\sqrt{1-4a})}{c}_1{\left(\frac{1}{x}\right)}^{\frac{1}{2}(1-\sqrt{1-4a})}{}_1{F}_1(\frac{1}{2}-\frac{1}{2}\sqrt{1-4a};1-\sqrt{1-4a};-\frac{2}{x})+2^{\frac{1}{2}(\sqrt{1-4a}+1)}{c}_2{\left(\frac{1}{x}\right)}^{\frac{1}{2}(\sqrt{1-4a}+1)}{}_1{F}_1(\frac{1}{2}\sqrt{1-4a}+\frac{1}{2};\sqrt{1-4a}+1;-\frac{2}{x})\}\right\}$$

✓ Maple : cpu = 0.034 (sec), leaf count = 57

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-x^{-1}}\sqrt{x^{-1}}{\mathit{I}}_{\frac{1}{2}\sqrt{1-4a}}\left(x^{-1}\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-x^{-1}}\sqrt{x^{-1}}{\mathit{K}}_{\frac{1}{2}\sqrt{1-4a}}\left(x^{-1}\right)\}$$