3.143   ODE No. 143

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

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

Mathematica: cpu = 0.008501 (sec), leaf count = 51 $$\left\{\{y(x)\to -\frac{\sqrt{4ab+1}(\frac{2c_1}{x^{\sqrt{4ab+1}}+c_1}-1)-1}{2ax}\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 49 $$\{y\left(x\right)=\frac{1}{2ax}(-\tanh (-\frac{\ln \left(x\right)}{2}\sqrt{4ab+1}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\sqrt{4ab+1})\sqrt{4ab+1}+1)\}$$