3.102   ODE No. 102

$$\boxed{{\displaystyle x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+x{\left(y\left(x\right)\right)}^2-y\left(x\right)-a{x}^3=0}}$$

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

Mathematica: cpu = 0.018502 (sec), leaf count = 36 $$\left\{\{y(x)\to \sqrt{a}x\tanh \left(\frac{1}{2}(2\sqrt{a}{c}_1+\sqrt{a}{x}^2)\right)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 24 $$\{y\left(x\right)=\tanh (\frac{x^2}{2}\sqrt{a}+\mathit{\_}\mathit{C}\mathit{1}\sqrt{a})x\sqrt{a}\}$$