3.526   ODE No. 526

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

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

Mathematica: cpu = 0.009501 (sec), leaf count = 45 $$\{\{y(x)\to \frac{1}{-c_1-x}\},\{y(x)\to c_1{e}^{\frac{x^2}{2}}\},\{y(x)\to c_1+\frac{x^3}{3}\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 32 $$\{y\left(x\right)={(-x+\mathit{\_}\mathit{C}\mathit{1})}^{-1},y\left(x\right)={\mathrm{e}}^{\frac{x^2}{2}}\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\frac{x^3}{3}+\mathit{\_}\mathit{C}\mathit{1}\}$$