2.537   ODE No. 537

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

$$(x^6+3xy(x{)}^2)y^{\prime }(x)-2x^{5}y(x)+x^3{y}^{\prime }(x{)}^3-3x^{2}y(x)y^{\prime }(x{)}^2-y(x{)}^3=0$$ ✓ Mathematica : cpu = 0.0358459 (sec), leaf count = 16

$$\left\{\{y(x)\to x(c_{1}x+c_1{}^3)\}\right\}$$ ✓ Maple : cpu = 4.172 (sec), leaf count = 250

$$\{y\left(x\right)=x^{\frac{5}{2}}\mathrm{RootOf}(c_1+{\int }_{}^{\mathit{\text{\_Z}}}\frac{18{(-\frac{4(-9\mathit{\text{\_a}}+\sqrt{81{\mathit{\text{\_a}}}^2+12})}{(27{\mathit{\text{\_a}}}^2+4)\sqrt{81{\mathit{\text{\_a}}}^2+12}})}^{\frac{2}{3}}{\mathit{\text{\_a}}}^2-18{(-\frac{4(-9\mathit{\text{\_a}}+\sqrt{81{\mathit{\text{\_a}}}^2+12})}{(27{\mathit{\text{\_a}}}^2+4)\sqrt{81{\mathit{\text{\_a}}}^2+12}})}^{\frac{1}{3}}{\mathit{\text{\_a}}}^2+\frac{8{(-\frac{4(-9\mathit{\text{\_a}}+\sqrt{81{\mathit{\text{\_a}}}^2+12})}{(27{\mathit{\text{\_a}}}^2+4)\sqrt{81{\mathit{\text{\_a}}}^2+12}})}^{\frac{2}{3}}}{3}-\frac{8{(-\frac{4(-9\mathit{\text{\_a}}+\sqrt{81{\mathit{\text{\_a}}}^2+12})}{(27{\mathit{\text{\_a}}}^2+4)\sqrt{81{\mathit{\text{\_a}}}^2+12}})}^{\frac{1}{3}}}{3}+\frac{8}{3}}{{(-\frac{4(-9\mathit{\text{\_a}}+\sqrt{81{\mathit{\text{\_a}}}^2+12})}{(27{\mathit{\text{\_a}}}^2+4)\sqrt{81{\mathit{\text{\_a}}}^2+12}})}^{\frac{1}{3}}(27{\mathit{\text{\_a}}}^2+4)\mathit{\text{\_a}}}d\mathit{\text{\_a}}-\ln \left(x\right)),y\left(x\right)=-\frac{2\sqrt{-3x}{x}^2}{9},y\left(x\right)=\frac{2\sqrt{-3x}{x}^2}{9}\}$$