8.76   ODE No. 1666

$$\boxed{{\displaystyle x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+bx{\mathrm{e}}^{y\left(x\right)}=0}}$$

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

Mathematica: cpu = 0.593575 (sec), leaf count = 26 $$\text{DSolve}[a{y}^{\prime }(x)+bx{e}^{y(x)}+x{y}^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.608 (sec), leaf count = 93 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}-2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{C}\mathit{1},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(b{\mathrm{e}}^{\mathit{\_}\mathit{a}}-2a+2){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(a-1){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=y\left(x\right)+2\ln \left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)={(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2)}^{-1}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\mathit{\_}\mathit{a}-2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{C}\mathit{1}\}])\}$$