8.45   ODE No. 1635

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

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

Mathematica: cpu = 101.517891 (sec), leaf count = 23 $$\text{DSolve}[a{y}^{\prime }(x{)}^2+by(x)+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.109 (sec), leaf count = 79 $$\{{\int }^{y\left(x\right)}-2\frac{a}{\sqrt{4{\mathrm{e}}^{-2a\mathit{\_}\mathit{a}}\mathit{\_}\mathit{C}\mathit{1}{a}^2-4\mathit{\_}\mathit{a}ab+2b}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}2\frac{a}{\sqrt{4{\mathrm{e}}^{-2a\mathit{\_}\mathit{a}}\mathit{\_}\mathit{C}\mathit{1}{a}^2-4\mathit{\_}\mathit{a}ab+2b}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$