2.244   ODE No. 244

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

$$x(2y(x)-x-1)y^{\prime }(x)+(-y(x)+2x-1)y(x)=0$$ ✓ Mathematica : cpu = 11.4828 (sec), leaf count = 484

$$\{\{y(x)\to -\frac{\sqrt[3]{2}x}{\sqrt[3]{27c_1{}^2{x}^2+\sqrt{(27c_1{}^2{x}^2+27c_1{}^{2}x){}^2-108c_1{}^3{x}^3}+27c_1{}^{2}x}}-\frac{\sqrt[3]{27c_1{}^2{x}^2+\sqrt{(27c_1{}^2{x}^2+27c_1{}^{2}x){}^2-108c_1{}^3{x}^3}+27c_1{}^{2}x}}{3\sqrt[3]{2}{c}_1}-\frac{c_{1}x+c_1}{c_1}\},\{y(x)\to \frac{(1+i\sqrt{3})x}{2^{2/3}\sqrt[3]{27c_1{}^2{x}^2+\sqrt{(27c_1{}^2{x}^2+27c_1{}^{2}x){}^2-108c_1{}^3{x}^3}+27c_1{}^{2}x}}+\frac{(1-i\sqrt{3})\sqrt[3]{27c_1{}^2{x}^2+\sqrt{(27c_1{}^2{x}^2+27c_1{}^{2}x){}^2-108c_1{}^3{x}^3}+27c_1{}^{2}x}}{6\sqrt[3]{2}{c}_1}-\frac{c_{1}x+c_1}{c_1}\},\{y(x)\to \frac{(1-i\sqrt{3})x}{2^{2/3}\sqrt[3]{27c_1{}^2{x}^2+\sqrt{(27c_1{}^2{x}^2+27c_1{}^{2}x){}^2-108c_1{}^3{x}^3}+27c_1{}^{2}x}}+\frac{(1+i\sqrt{3})\sqrt[3]{27c_1{}^2{x}^2+\sqrt{(27c_1{}^2{x}^2+27c_1{}^{2}x){}^2-108c_1{}^3{x}^3}+27c_1{}^{2}x}}{6\sqrt[3]{2}{c}_1}-\frac{c_{1}x+c_1}{c_1}\}\}$$ ✓ Maple : cpu = 0.095 (sec), leaf count = 391

$$\{y\left(x\right)=\frac{3}{80\mathit{\_}\mathit{C}\mathit{1}}({\left(x(\sqrt{5}\sqrt{\frac{80{(1+x)}^2\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}-20x-20){\mathit{\_}\mathit{C}\mathit{1}}^2\right)}^{\frac{2}{3}}(i\sqrt{3}-1)\sqrt[3]{5}-(x(1+i\sqrt{3})5^{\frac{2}{3}}+\frac{80+80x}{3}\sqrt[3]{-20x(-1/20\sqrt{5}\sqrt{\frac{80{(1+x)}^2\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}+x+1){\mathit{\_}\mathit{C}\mathit{1}}^2})\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{-20x(-1/20\sqrt{5}\sqrt{\frac{80{(1+x)}^2\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}+x+1){\mathit{\_}\mathit{C}\mathit{1}}^2}},y\left(x\right)=-\frac{3}{80\mathit{\_}\mathit{C}\mathit{1}}({\left(x(\sqrt{5}\sqrt{\frac{80{(1+x)}^2\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}-20x-20){\mathit{\_}\mathit{C}\mathit{1}}^2\right)}^{\frac{2}{3}}(1+i\sqrt{3})\sqrt[3]{5}-(x(i\sqrt{3}-1)5^{\frac{2}{3}}-\frac{80+80x}{3}\sqrt[3]{-20x(-1/20\sqrt{5}\sqrt{\frac{80{(1+x)}^2\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}+x+1){\mathit{\_}\mathit{C}\mathit{1}}^2})\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{-20x(-1/20\sqrt{5}\sqrt{\frac{80{(1+x)}^2\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}+x+1){\mathit{\_}\mathit{C}\mathit{1}}^2}},y\left(x\right)=\frac{3\sqrt[3]{5}}{40\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{x(\sqrt{5}\sqrt{\frac{80\mathit{\_}\mathit{C}\mathit{1}{x}^2+160\mathit{\_}\mathit{C}\mathit{1}x+80\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}-20x-20){\mathit{\_}\mathit{C}\mathit{1}}^2}+\frac{3x{5}^{2/3}}{40}\frac{1}{\sqrt[3]{x(\sqrt{5}\sqrt{\frac{80\mathit{\_}\mathit{C}\mathit{1}{x}^2+160\mathit{\_}\mathit{C}\mathit{1}x+80\mathit{\_}\mathit{C}\mathit{1}-x}{\mathit{\_}\mathit{C}\mathit{1}}}-20x-20){\mathit{\_}\mathit{C}\mathit{1}}^2}}-1-x\}$$