2.1828   ODE No. 1828

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

$$2(x^2+1)y^{″}(x{)}^2-x(4y^{\prime }(x)+x)y^{″}(x)+2y^{\prime }(x)(y^{\prime }(x)+x)-2y(x)=0$$ ✓ Mathematica : cpu = 0.0073533 (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 = 1.424 (sec), leaf count = 59

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^2}{2}+\mathit{\_}\mathit{C}\mathit{2}x+{\mathit{\_}\mathit{C}\mathit{1}}^2+{\mathit{\_}\mathit{C}\mathit{2}}^2,y\left(x\right)=\frac{x}{2}(\mathit{\_}\mathit{C}\mathit{1}+\frac{\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)}{4})\sqrt{x^2+1}-\frac{3x^2}{16}+{\mathit{\_}\mathit{C}\mathit{1}}^2+\frac{\mathit{\_}\mathit{C}\mathit{1}\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)}{2}+\frac{{\left(\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(x\right)\right)}^2}{16}\}$$