3.309   ODE No. 309

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

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

Mathematica: cpu = 0.011001 (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 = 0.047 (sec), leaf count = 113 $$\{y\left(x\right)=-\frac{1}{2}\sqrt{-2-2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}},y\left(x\right)=\frac{1}{2}\sqrt{-2-2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}},y\left(x\right)=-\frac{1}{2}\sqrt{-2+2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}},y\left(x\right)=\frac{1}{2}\sqrt{-2+2\sqrt{4x^4+4x^2+8\mathit{\_}\mathit{C}\mathit{1}+1}}\}$$