3.303   ODE No. 303

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

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

Mathematica: cpu = 0.044006 (sec), leaf count = 25 $$\text{Solve}[xy(x)-\frac{1}{xy(x)}-2\log (y(x))=c_1,y(x)]$$

Maple: cpu = 0.125 (sec), leaf count = 34 $$\{y\left(x\right)=\frac{{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(x\right)-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+2\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+1)}}{x}\}$$