2.1145   ODE No. 1145

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

$$y(x)(\text{a0}x+\text{b0})+(\text{a1}x+\text{b1})y^{\prime }(x)+(\text{a2}x+\text{b2})y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.37844 (sec), leaf count = 398

$$\left\{\{y(x)\to c_{1}U(-\frac{\text{b2}{\text{a1}}^2-\text{a2}\text{b1}\text{a1}-\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}\text{b2}\text{a1}+2{\text{a2}}^2\text{b0}+\text{a2}\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}\text{b1}-2\text{a0}\text{a2}\text{b2}-2{\text{a2}}^2\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}{2{\text{a2}}^2\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}},\frac{{\text{a2}}^2-\text{b1}\text{a2}+\text{a1}\text{b2}}{{\text{a2}}^2}+1,\frac{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}\text{b2}}{{\text{a2}}^2}+\frac{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}x}{\text{a2}})\exp \left(\frac{x(-\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}-\text{a1})+\frac{2(\text{a1}\text{b2}+{\text{a2}}^2-\text{a2}\text{b1})\log (\text{a2}x+\text{b2})}{\text{a2}}}{2\text{a2}}\right)+c_2{L}_{\frac{-2{\text{a2}}^2\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}+\text{a2}\text{b1}\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}-\text{a1}\text{b2}\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}-2\text{a0}\text{a2}\text{b2}+{\text{a1}}^2\text{b2}-\text{a1}\text{a2}\text{b1}+2{\text{a2}}^2\text{b0}}{2{\text{a2}}^2\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}}^{\frac{\text{a1}\text{b2}+{\text{a2}}^2-\text{a2}\text{b1}}{{\text{a2}}^2}}(\frac{\text{b2}\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}{{\text{a2}}^2}+\frac{x\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}{\text{a2}})\exp \left(\frac{x(-\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}-\text{a1})+\frac{2(\text{a1}\text{b2}+{\text{a2}}^2-\text{a2}\text{b1})\log (\text{a2}x+\text{b2})}{\text{a2}}}{2\text{a2}}\right)\}\right\}$$

✓ Maple : cpu = 0.201 (sec), leaf count = 287

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x}{2\mathit{a}\mathit{2}}(\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}+\mathit{a}\mathit{1})}\mathit{M}(\frac{1}{2{\mathit{a}\mathit{2}}^2}((\mathit{a}\mathit{1}\mathit{b}\mathit{2}+2{\mathit{a}\mathit{2}}^2-\mathit{a}\mathit{2}\mathit{b}\mathit{1})\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}-2{\mathit{a}\mathit{2}}^2\mathit{b}\mathit{0}+(2\mathit{a}\mathit{0}\mathit{b}\mathit{2}+\mathit{a}\mathit{1}\mathit{b}\mathit{1})\mathit{a}\mathit{2}-{\mathit{a}\mathit{1}}^2\mathit{b}\mathit{2})\frac{1}{\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}},\frac{\mathit{a}\mathit{1}\mathit{b}\mathit{2}+2{\mathit{a}\mathit{2}}^2-\mathit{a}\mathit{2}\mathit{b}\mathit{1}}{{\mathit{a}\mathit{2}}^2},\frac{\mathit{a}\mathit{2}x+\mathit{b}\mathit{2}}{{\mathit{a}\mathit{2}}^2}\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}){(\mathit{a}\mathit{2}x+\mathit{b}\mathit{2})}^{\frac{\mathit{a}\mathit{1}\mathit{b}\mathit{2}+{\mathit{a}\mathit{2}}^2-\mathit{a}\mathit{2}\mathit{b}\mathit{1}}{{\mathit{a}\mathit{2}}^2}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x}{2\mathit{a}\mathit{2}}(\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}+\mathit{a}\mathit{1})}\mathit{U}(\frac{1}{2{\mathit{a}\mathit{2}}^2}((\mathit{a}\mathit{1}\mathit{b}\mathit{2}+2{\mathit{a}\mathit{2}}^2-\mathit{a}\mathit{2}\mathit{b}\mathit{1})\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}-2{\mathit{a}\mathit{2}}^2\mathit{b}\mathit{0}+(2\mathit{a}\mathit{0}\mathit{b}\mathit{2}+\mathit{a}\mathit{1}\mathit{b}\mathit{1})\mathit{a}\mathit{2}-{\mathit{a}\mathit{1}}^2\mathit{b}\mathit{2})\frac{1}{\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}},\frac{\mathit{a}\mathit{1}\mathit{b}\mathit{2}+2{\mathit{a}\mathit{2}}^2-\mathit{a}\mathit{2}\mathit{b}\mathit{1}}{{\mathit{a}\mathit{2}}^2},\frac{\mathit{a}\mathit{2}x+\mathit{b}\mathit{2}}{{\mathit{a}\mathit{2}}^2}\sqrt{-4\mathit{a}\mathit{0}\mathit{a}\mathit{2}+{\mathit{a}\mathit{1}}^2}){(\mathit{a}\mathit{2}x+\mathit{b}\mathit{2})}^{\frac{\mathit{a}\mathit{1}\mathit{b}\mathit{2}+{\mathit{a}\mathit{2}}^2-\mathit{a}\mathit{2}\mathit{b}\mathit{1}}{{\mathit{a}\mathit{2}}^2}}\}$$