3.168   ODE No. 168

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

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

Mathematica: cpu = 0.093012 (sec), leaf count = 234 $$\left\{\{y(x)\to \frac{3(x^2-4)(c_1(\frac{x{P}_{-\frac{1}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right)}{6{(x^2-4)}^{11/12}}+\frac{\sqrt[12]{x^2-4}(\frac{1}{2}{P}_{\frac{5}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right)-\frac{5}{12}x{P}_{-\frac{1}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right))}{2(\frac{x^2}{4}-1)})+\frac{x{Q}_{-\frac{1}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right)}{6{(x^2-4)}^{11/12}}+\frac{\sqrt[12]{x^2-4}(\frac{1}{2}{Q}_{\frac{5}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right)-\frac{5}{12}x{Q}_{-\frac{1}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right))}{2(\frac{x^2}{4}-1)})}{c_1\sqrt[12]{x^2-4}{P}_{-\frac{1}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right)+\sqrt[12]{x^2-4}{Q}_{-\frac{1}{6}}^{\frac{1}{3}}\left(\frac{x}{2}\right)}\}\right\}$$

Maple: cpu = 0.140 (sec), leaf count = 140 $$\{y\left(x\right)=-3(x+2)(\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,4/3,-1/3,0,\frac{25}{36},4{(x+2)}^{-1})\mathit{\_}\mathit{C}\mathit{1}-1/3{(-x/4-1/2)}^{4/3}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,-4/3,-1/3,0,\frac{25}{36},4{(x+2)}^{-1})){(4\mathit{\_}\mathit{C}\mathit{1}(x-5/4)(x+2)\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,4/3,-1/3,0,\frac{25}{36},4{(x+2)}^{-1})-{(-x/4-1/2)}^{4/3}(x+2)\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,-4/3,-1/3,0,\frac{25}{36},4{(x+2)}^{-1})+12(\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}\mathit{P}\mathit{r}\mathit{i}\mathit{m}\mathit{e}(0,4/3,-1/3,0,\frac{25}{36},4{(x+2)}^{-1})\mathit{\_}\mathit{C}\mathit{1}-1/3{(-x/4-1/2)}^{4/3}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}\mathit{P}\mathit{r}\mathit{i}\mathit{m}\mathit{e}(0,-4/3,-1/3,0,\frac{25}{36},4{(x+2)}^{-1}))(x-2))}^{-1}\}$$