3.141   ODE No. 141

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

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

Mathematica: cpu = 0.026003 (sec), leaf count = 67 $$\left\{\{y(x)\to -\frac{\sqrt{a^2-2a-4b+1}(\frac{2c_1}{x^{\sqrt{a^2-2a-4b+1}}+c_1}-1)-1}{2x}-\frac{a}{2x}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 64 $$\{y\left(x\right)=\frac{1}{2x}(-\tanh (-\frac{\ln \left(x\right)}{2}\sqrt{a^2-2a-4b+1}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\sqrt{a^2-2a-4b+1})\sqrt{a^2-2a-4b+1}-a+1)\}$$