2.1190   ODE No. 1190

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

$$y(x)(ax+b)+x^2{y}^{″}(x)+x^2{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0319082 (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 = 0.104 (sec), leaf count = 41

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