8.4   ODE No. 1594

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-6{\left(y\left(x\right)\right)}^2+4y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.366546 (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 = 0.110 (sec), leaf count = 59 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3-4{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3-4{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$