3.289   ODE No. 289

$$\boxed{{\displaystyle {(6y\left(x\right)-x)}^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-6{\left(y\left(x\right)\right)}^2+2xy\left(x\right)+a=0}}$$

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

Mathematica: cpu = 0.016502 (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 = 0.031 (sec), leaf count = 115 $$\{y\left(x\right)=\frac{1}{6}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{x}{6},y\left(x\right)=-\frac{1}{12}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}-\frac{i}{12}\sqrt{3}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{x}{6},y\left(x\right)=-\frac{1}{12}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{i}{12}\sqrt{3}\sqrt[3]{-x^3-18ax-18\mathit{\_}\mathit{C}\mathit{1}}+\frac{x}{6}\}$$