2.1594   ODE No. 1594

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

$$y^{″}(x)-6y(x{)}^2+4y(x)=0$$ ✓ Mathematica : cpu = 0.366401 (sec), leaf count = 373

$$\text{Solve}[\frac{4(\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},2]-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3])(y(x)-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},1])(y(x)-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},2])(y(x)-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3])F({\sin }^{-1}\left(\sqrt{\frac{\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3]-y(x)}{\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3]-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},2]}}\right)|\frac{\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},2]-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3]}{\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},1]-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3]}){}^2}{(c_1+4y(x{)}^3-4y(x{)}^2)(\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3]-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},1])(\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},3]-\text{Root}[4{\mathrm{\#}\text{1}}^3-4{\mathrm{\#}\text{1}}^2+c_1\mathrm{\&},2])}=(c_2+x){}^2,y(x)]$$

✓ Maple : cpu = 0.213 (sec), leaf count = 59

$$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3-4{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3-4{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$