2.1830   ODE No. 1830

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

$$(2-9x)x^2{y}^{″}(x{)}^2-6(1-6x)x{y}^{\prime }(x)y^{″}(x)-36x{y}^{\prime }(x{)}^2+6y(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0221828 (sec), leaf count = 24

$$\left\{\{y(x)\to \frac{c_1{}^2{x}^3}{c_2}+c_{1}x+c_2\}\right\}$$ ✓ Maple : cpu = 1.432 (sec), leaf count = 308

$$\{y\left(x\right)=0,y\left(x\right)=\frac{27\sqrt{5}\mathit{\_}\mathit{C}\mathit{1}\sqrt{4}x}{4}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{-\frac{5\sqrt{9}}{18}}\sqrt{(\frac{4}{5}+\sqrt{16}(x-\frac{1}{5})\frac{1}{\sqrt{9x^2-2x}})\frac{1}{\sqrt{-\frac{{(4x-1)}^2}{9x^2-2x}}}}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{-\frac{2\sqrt{9}}{9}}\sqrt{4x-1}{\mathrm{e}}^{-\frac{\sqrt{16}-4}{2}\sqrt{9x^2-2x}},y\left(x\right)=\frac{\sqrt{5}\mathit{\_}\mathit{C}\mathit{1}\sqrt{4}x}{135}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{\frac{5\sqrt{9}}{18}}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{\frac{2\sqrt{9}}{9}}\sqrt{4x-1}{\mathrm{e}}^{\frac{\sqrt{16}-4}{2}\sqrt{9x^2-2x}}\frac{1}{\sqrt{(\frac{4}{5}+\sqrt{16}(x-\frac{1}{5})\frac{1}{\sqrt{9x^2-2x}})\frac{1}{\sqrt{-\frac{{(4x-1)}^2}{9x^2-2x}}}}},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^3+\mathit{\_}\mathit{C}\mathit{2}x+\frac{{\mathit{\_}\mathit{C}\mathit{2}}^2}{\mathit{\_}\mathit{C}\mathit{1}}\}$$