2.309   ODE No. 309

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

$$-2x^3+(2y(x{)}^3+y(x))y^{\prime }(x)-x=0$$ ✓ Mathematica : cpu = 0.0146281 (sec), leaf count = 151

$$\{\{y(x)\to -\frac{\sqrt{-\sqrt{8c_1+4x^4+4x^2+1}-1}}{\sqrt{2}}\},\{y(x)\to \frac{\sqrt{-\sqrt{8c_1+4x^4+4x^2+1}-1}}{\sqrt{2}}\},\{y(x)\to -\frac{\sqrt{\sqrt{8c_1+4x^4+4x^2+1}-1}}{\sqrt{2}}\},\{y(x)\to \frac{\sqrt{\sqrt{8c_1+4x^4+4x^2+1}-1}}{\sqrt{2}}\}\}$$

✓ Maple : cpu = 0.04 (sec), leaf count = 113

$$\{y\left(x\right)=-\frac{1}{2}\sqrt{-2-2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}},y\left(x\right)=\frac{1}{2}\sqrt{-2-2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}},y\left(x\right)=-\frac{1}{2}\sqrt{-2+2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}},y\left(x\right)=\frac{1}{2}\sqrt{-2+2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}}\}$$