4.188   ODE No. 1188

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

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

Mathematica: cpu = 0.082511 (sec), leaf count = 266 $$\left\{\{y(x)\to c_1{i}^{-\sqrt{a^2-2a-4c+1}+a-1}{b}^{\frac{1}{2}(-\sqrt{a^2-2a-4c+1}+a-1)}{\left(\frac{1}{x}\right)}^{\frac{1}{2}(-\sqrt{a^2-2a-4c+1}+a-1)}{}_1{F}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{1}{2};1-\sqrt{a^2-2a-4c+1};\frac{b}{x})+c_2{i}^{\sqrt{a^2-2a-4c+1}+a-1}{b}^{\frac{1}{2}(\sqrt{a^2-2a-4c+1}+a-1)}{\left(\frac{1}{x}\right)}^{\frac{1}{2}(\sqrt{a^2-2a-4c+1}+a-1)}{}_1{F}_1(\frac{a}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{1}{2};\sqrt{a^2-2a-4c+1}+1;\frac{b}{x})\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 135 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{a}{2}+\frac{1}{2}}\mathit{M}(-\frac{1}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{a}{2},1+\sqrt{a^2-2a-4c+1},\frac{b}{x})+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{a}{2}+\frac{1}{2}}\mathit{U}(-\frac{1}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{a}{2},1+\sqrt{a^2-2a-4c+1},\frac{b}{x})\}$$