3.103   ODE No. 103

$$\boxed{{\displaystyle x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+x{\left(y\left(x\right)\right)}^2-(2x^2+1)y\left(x\right)-x^3=0}}$$

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

Mathematica: cpu = 0.097012 (sec), leaf count = 90 $$\left\{\{y(x)\to \frac{x(e^{2\sqrt{2}{c}_1}-\sqrt{2}{e}^{2\sqrt{2}{c}_1}+e^{\sqrt{2}{x}^2}+\sqrt{2}{e}^{\sqrt{2}{x}^2})}{e^{2\sqrt{2}{c}_1}+e^{\sqrt{2}{x}^2}}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 29 $$\{y\left(x\right)=\frac{\sqrt{2}x}{2}(\sqrt{2}+2\tanh \left(1/2(x^2+2\mathit{\_}\mathit{C}\mathit{1})\sqrt{2}\right))\}$$