2.1296   ODE No. 1296

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

$$y(x)(\text{a0}{x}^2+\text{b0}x+\text{c0})+(\text{a1}{x}^2+\text{b1}x)y^{\prime }(x)+\text{a2}{x}^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.597203 (sec), leaf count = 272

$$\left\{\{y(x)\to e^{-\frac{x(\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}+\text{a1})}{2\text{a2}}}{x}^{\frac{\sqrt{{\text{a2}}^2-2\text{a2}(\text{b1}+2\text{c0})+{\text{b1}}^2}+\text{a2}-\text{b1}}{2\text{a2}}}(c_{1}U(\frac{-\frac{2\text{b0}\text{a2}}{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}+\text{a2}+\frac{\text{a1}\text{b1}}{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}+\sqrt{{\text{a2}}^2-2(\text{b1}+2\text{c0})\text{a2}+{\text{b1}}^2}}{2\text{a2}},\frac{\text{a2}+\sqrt{{\text{a2}}^2-2(\text{b1}+2\text{c0})\text{a2}+{\text{b1}}^2}}{\text{a2}},\frac{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}x}{\text{a2}})+c_2{L}_{-\frac{-\frac{2\text{b0}\text{a2}}{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}+\text{a2}+\frac{\text{a1}\text{b1}}{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}}+\sqrt{{\text{a2}}^2-2(\text{b1}+2\text{c0})\text{a2}+{\text{b1}}^2}}{2\text{a2}}}^{\frac{\sqrt{{\text{a2}}^2-2(\text{b1}+2\text{c0})\text{a2}+{\text{b1}}^2}}{\text{a2}}}\left(\frac{\sqrt{{\text{a1}}^2-4\text{a0}\text{a2}}x}{\text{a2}}\right))\}\right\}$$

✓ Maple : cpu = 0.359 (sec), leaf count = 150

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