3.546   ODE No. 546

$$\boxed{{\displaystyle {\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^4+3(x-1){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-3(2y\left(x\right)-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+3x=0}}$$

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.125 (sec), leaf count = 245 $$\{y\left(x\right)=-x+\frac{5}{6},y\left(x\right)=x+\frac{1}{6},y\left(x\right)=\frac{x}{6}(3{(-\mathit{\_}\mathit{C}\mathit{1}/2-1/2\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^2+3){(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}-\frac{1}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^{-1}+\frac{1}{6}({(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}-\frac{1}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^4-3{(-\mathit{\_}\mathit{C}\mathit{1}/2-1/2\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^2-\frac{3\mathit{\_}\mathit{C}\mathit{1}}{2}-\frac{3}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x}){(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}-\frac{1}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^{-1},y\left(x\right)=\frac{x}{6}(3{(-\mathit{\_}\mathit{C}\mathit{1}/2+1/2\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^2+3){(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}+\frac{1}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^{-1}+\frac{1}{6}({(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}+\frac{1}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^4-3{(-\mathit{\_}\mathit{C}\mathit{1}/2+1/2\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^2-\frac{3\mathit{\_}\mathit{C}\mathit{1}}{2}+\frac{3}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x}){(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}+\frac{1}{2}\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+4x})}^{-1}\}$$