3.976   ODE No. 976

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)({\left(y\left(x\right)\right)}^2{x}^7+y\left(x\right)x^4+x-3)}{x}=0}}$$

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

Mathematica: cpu = 0.076010 (sec), leaf count = 101 $$\text{Solve}[-\frac{7}{3}\text{RootSum}[-7{\mathrm{\#}\text{1}}^3+6\sqrt[3]{-7}\mathrm{\#}\text{1}-7\mathrm{\&},\frac{\log (\frac{3x^{6}y(x)+x^3}{\sqrt[3]{7}\sqrt[3]{-x^9}}-\mathrm{\#}\text{1})}{2\sqrt[3]{-7}-7{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{7^{2/3}{(-x^9)}^{2/3}}{9x^5},y(x)]$$

Maple: cpu = 0.172 (sec), leaf count = 57 $$\{y\left(x\right)=\frac{1}{2x^3}(\sqrt{3}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\sqrt{3}\ln \left(\frac{9{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+9}{7{(-3\tan \left(\mathit{\_}\mathit{Z}\right)+\sqrt{3})}^2}\right)+3\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}-2\sqrt{3}x-2\mathit{\_}\mathit{Z})\right)-1)\}$$