2.289   ODE No. 289

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

$$a+(6y(x)-x{)}^2{y}^{\prime }(x)-6y(x{)}^2+2xy(x)=0$$ ✓ Mathematica : cpu = 0.0188803 (sec), leaf count = 115

$$\{\{y(x)\to \frac{1}{6}(\sqrt[3]{-18ax+18c_1-x^3}+x)\},\{y(x)\to \frac{x}{6}-\frac{1}{12}(1-i\sqrt{3})\sqrt[3]{-18ax+18c_1-x^3}\},\{y(x)\to \frac{x}{6}-\frac{1}{12}(1+i\sqrt{3})\sqrt[3]{-18ax+18c_1-x^3}\}\}$$

✓ Maple : cpu = 0.035 (sec), leaf count = 115

$$\{y\left(x\right)=\frac{1}{6}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{x}{6},y\left(x\right)=-\frac{1}{12}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}-\frac{i}{12}\sqrt{3}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{x}{6},y\left(x\right)=-\frac{1}{12}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{i}{12}\sqrt{3}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{x}{6}\}$$