8.50   ODE No. 1640

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

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

Mathematica: cpu = 200.467956 (sec), leaf count = 25 $$\text{DSolve}[ay(x)y^{\prime }(x{)}^2+by(x)+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.109 (sec), leaf count = 70 $$\{{\int }^{y\left(x\right)}a\frac{1}{\sqrt{a({\mathrm{e}}^{-{\mathit{\_}\mathit{a}}^{2}a}\mathit{\_}\mathit{C}\mathit{1}a-b)}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-a\frac{1}{\sqrt{a({\mathrm{e}}^{-{\mathit{\_}\mathit{a}}^{2}a}\mathit{\_}\mathit{C}\mathit{1}a-b)}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$