4.190   ODE No. 1190

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

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

Mathematica: cpu = 0.030004 (sec), leaf count = 122 $$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}((\sqrt{1-4b}+1)\log (x)-2x)}U(\frac{1}{2}(-2a+\sqrt{1-4b}+1),\sqrt{1-4b}+1,x)+c_2{e}^{\frac{1}{2}((\sqrt{1-4b}+1)\log (x)-2x)}{L}_{\frac{1}{2}(2a-\sqrt{1-4b}-1)}^{\sqrt{1-4b}}(x)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 41 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x}{2}}{\mathit{M}}_{a,\frac{1}{2}\sqrt{1-4b}}\left(x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x}{2}}{\mathit{W}}_{a,\frac{1}{2}\sqrt{1-4b}}\left(x\right)\}$$