8.168   ODE No. 1758

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

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

Mathematica: cpu = 0.062008 (sec), leaf count = 36 $$\left\{\{y(x)\to \frac{(c_1(-(a+c))(-c_2-x)){}^{\frac{a}{a+c}}-b}{a}\}\right\}$$

Maple: cpu = 1.529 (sec), leaf count = 88 $$\{y\left(x\right)=-\frac{1}{a}(-\mathit{\_}\mathit{C}\mathit{1}ax-\mathit{\_}\mathit{C}\mathit{1}xc+b{\left({\left(\frac{1}{(a+c)(\mathit{\_}\mathit{C}\mathit{1}x+\mathit{\_}\mathit{C}\mathit{2})}\right)}^{\frac{c}{a}{(1+\frac{c}{a})}^{-1}}\right)}^{-1}-\mathit{\_}\mathit{C}\mathit{2}a-\mathit{\_}\mathit{C}\mathit{2}c){\left(\frac{1}{(a+c)(\mathit{\_}\mathit{C}\mathit{1}x+\mathit{\_}\mathit{C}\mathit{2})}\right)}^{\frac{c}{a}{(1+\frac{c}{a})}^{-1}}\}$$