8.238   ODE No. 1828

$$\boxed{{\displaystyle 2(x^2+1){\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)}^2-x\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)(x+4\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right))+2(x+\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-2y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.012502 (sec), leaf count = 32 $$\left\{\{y(x)\to -\frac{1}{2}\sqrt{c_2-c_1^2}{x}^2+c_{1}x+c_2\}\right\}$$

Maple: cpu = 1.045 (sec), leaf count = 20 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^2}{2}+\mathit{\_}\mathit{C}\mathit{2}x+{\mathit{\_}\mathit{C}\mathit{1}}^2+{\mathit{\_}\mathit{C}\mathit{2}}^2\}$$