2.1830   ODE No. 1830

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

$$(2-9x)x^2{y}^{″}(x{)}^2+6y(x)y^{″}(x)-36x{y}^{\prime }(x{)}^2-6(1-6x)x{y}^{\prime }(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0280316 (sec), leaf count = 24

$$\left\{\{y(x)\to \frac{c_1^2{x}^3}{c_2}+c_{1}x+c_2\}\right\}$$

✓ Maple : cpu = 0.904 (sec), leaf count = 312

$$\{y\left(x\right)=27\mathit{\_}\mathit{C}\mathit{1}{((9x-1)\sqrt{9}+9\sqrt{(9x-2)x})}^{-\frac{5\sqrt{9}}{18}}\sqrt{1(1/2\frac{(-1/2+5/2x)\sqrt{16}}{\sqrt{(9x-2)x}}+1)\frac{1}{\sqrt{\frac{-16x^2+8x-1}{(9x-2)x}}}}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{-2/9\sqrt{9}}\sqrt{4x-1}x{\mathrm{e}}^{-1/2\sqrt{16}\sqrt{(9x-2)x}+2\sqrt{9x^2-2x}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}x}{27}{((9x-1)\sqrt{9}+9\sqrt{(9x-2)x})}^{\frac{5\sqrt{9}}{18}}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{\frac{2\sqrt{9}}{9}}\sqrt{4x-1}{\mathrm{e}}^{\frac{\sqrt{16}}{2}\sqrt{(9x-2)x}-2\sqrt{9x^2-2x}}\frac{1}{\sqrt{1(\frac{\sqrt{16}}{2}(-\frac{1}{2}+\frac{5x}{2})\frac{1}{\sqrt{(9x-2)x}}+1)\frac{1}{\sqrt{\frac{-16x^2+8x-1}{(9x-2)x}}}}},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{2}{x}^3+\mathit{\_}\mathit{C}\mathit{1}x+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{\mathit{\_}\mathit{C}\mathit{2}}\}$$