8.107   ODE No. 1697

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

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

Mathematica: cpu = 0.062508 (sec), leaf count = 94 $$\{\{y(x)\to -\frac{\sqrt{2a^2{c}_{2}x+a^2{c}_2^2+a^2{x}^2-e^{2c_1}}}{\sqrt{a}}\},\{y(x)\to \frac{\sqrt{2a^2{c}_{2}x+a^2{c}_2^2+a^2{x}^2-e^{2c_1}}}{\sqrt{a}}\}\}$$

Maple: cpu = 1.669 (sec), leaf count = 39 $$\{y\left(x\right)=\sqrt{a{x}^2-2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2}},y\left(x\right)=-\sqrt{a{x}^2-2\mathit{\_}\mathit{C}\mathit{1}x+2\mathit{\_}\mathit{C}\mathit{2}}\}$$