2.1120   ODE No. 1120

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

$$(ax+b)y^{\prime }(x)+y(x)(cx+d)+x{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0693585 (sec), leaf count = 166

$$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}x(-\sqrt{a^2-4c}-a)}U(-\frac{-ab-\sqrt{a^2-4c}b+2d}{2\sqrt{a^2-4c}},b,\sqrt{a^2-4c}x)+c_2{e}^{\frac{1}{2}x(-\sqrt{a^2-4c}-a)}{L}_{\frac{-b\sqrt{a^2-4c}-ab+2d}{2\sqrt{a^2-4c}}}^{b-1}\left(x\sqrt{a^2-4c}\right)\}\right\}$$

✓ Maple : cpu = 0.225 (sec), leaf count = 123

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