2.1020   ODE No. 1020

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

$$y(x)(a{e}^{2x}+b{e}^x+c)+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.568417 (sec), leaf count = 180

$$\left\{\{y(x)\to c_1{e}^{i(\sqrt{c}\log \left(e^x\right)-\sqrt{a}{e}^x)}U(\frac{i(b-i\sqrt{a}+2\sqrt{a}\sqrt{c})}{2\sqrt{a}},2i\sqrt{c}+1,2i\sqrt{a}{e}^x)+c_2{e}^{i(\sqrt{c}\log \left(e^x\right)-\sqrt{a}{e}^x)}{L}_{-\frac{i(b-i\sqrt{a}+2\sqrt{a}\sqrt{c})}{2\sqrt{a}}}^{2i\sqrt{c}}\left(2i\sqrt{a}{e}^x\right)\}\right\}$$ ✓ Maple : cpu = 1.243 (sec), leaf count = 58

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