3.940   ODE No. 940

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)\ln \left(x\right)x+x^2\ln \left(x\right)-2xy\left(x\right)-x^2-{\left(y\left(x\right)\right)}^2-{\left(y\left(x\right)\right)}^3+3x{\left(y\left(x\right)\right)}^2\ln \left(x\right)-3x^2{(\ln \left(x\right))}^{2}y\left(x\right)+x^3{(\ln \left(x\right))}^3}{x(-y\left(x\right)+x\ln \left(x\right)-x)}=0}}$$

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

Mathematica: cpu = 0.022003 (sec), leaf count = 80 $$\{\{y(x)\to -\frac{1}{x(-\frac{1}{x^2\sqrt{c_1-2x}}-\frac{1}{x^2})}-x+x\log (x)\},\{y(x)\to -\frac{1}{x(\frac{1}{x^2\sqrt{c_1-2x}}-\frac{1}{x^2})}-x+x\log (x)\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 63 $$\{y\left(x\right)=x(\ln \left(x\right)\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}-\ln \left(x\right)+1){(\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}-1)}^{-1},y\left(x\right)=x(\ln \left(x\right)\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}+\ln \left(x\right)-1){(\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}+1)}^{-1}\}$$