2.1665   ODE No. 1665

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

$$x{y}^{″}(x)+2y^{\prime }(x)+x{e}^{y(x)}=0$$ ✗ Mathematica : cpu = 0.356855 (sec), leaf count = 0 , could not solve

DSolve[E^y[x]*x + 2*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.628 (sec), leaf count = 84

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}-2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{C}\mathit{1},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=({\mathrm{e}}^{\mathit{\_}\mathit{a}}-2){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=y\left(x\right)+2\ln \left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)={(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2)}^{-1}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\mathit{\_}\mathit{a}-2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{C}\mathit{1}\}])\}$$