8.240   ODE No. 1830

$$\boxed{{\displaystyle x^2(2-9x){\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)}^2-6x(1-6x)\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+6\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-36x{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 0.029004 (sec), leaf count = 24 $$\left\{\{y(x)\to \frac{c_1^2{x}^3}{c_2}+c_{1}x+c_2\}\right\}$$

Maple: cpu = 0.390 (sec), leaf count = 312 $$\{y\left(x\right)=27\mathit{\_}\mathit{C}\mathit{1}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{-2/9\sqrt{9}}{((9x-1)\sqrt{9}+9\sqrt{x(9x-2)})}^{-\frac{5\sqrt{9}}{18}}\sqrt{1(1+1/2\frac{(-1/2+5/2x)\sqrt{16}}{\sqrt{x(9x-2)}})\frac{1}{\sqrt{\frac{-16x^2+8x-1}{x(9x-2)}}}}x\sqrt{4x-1}{\mathrm{e}}^{2\sqrt{9x^2-2x}-1/2\sqrt{16}\sqrt{x(9x-2)}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}x}{27}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{\frac{2\sqrt{9}}{9}}{((9x-1)\sqrt{9}+9\sqrt{x(9x-2)})}^{\frac{5\sqrt{9}}{18}}\sqrt{4x-1}{\mathrm{e}}^{-2\sqrt{9x^2-2x}+\frac{\sqrt{16}}{2}\sqrt{x(9x-2)}}\frac{1}{\sqrt{1(1+\frac{\sqrt{16}}{2}(-\frac{1}{2}+\frac{5x}{2})\frac{1}{\sqrt{x(9x-2)}})\frac{1}{\sqrt{\frac{-16x^2+8x-1}{x(9x-2)}}}}},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^3+\mathit{\_}\mathit{C}\mathit{2}x+\frac{{\mathit{\_}\mathit{C}\mathit{2}}^2}{\mathit{\_}\mathit{C}\mathit{1}}\}$$