3.878   ODE No. 878

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{1+{\left(y\left(x\right)\right)}^4-8ax{\left(y\left(x\right)\right)}^2+16a^2{x}^2+{\left(y\left(x\right)\right)}^6-12{\left(y\left(x\right)\right)}^{4}ax+48{\left(y\left(x\right)\right)}^2{a}^2{x}^2-64a^3{x}^3}{y\left(x\right)}=0}}$$

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

Mathematica: cpu = 0.262533 (sec), leaf count = 130 $$\text{Solve}[2a(x-\frac{1}{2}\text{RootSum}[64{\mathrm{\#}\text{1}}^3{a}^3-48{\mathrm{\#}\text{1}}^2{a}^{2}y(x{)}^2-16{\mathrm{\#}\text{1}}^2{a}^2+12\mathrm{\#}\text{1}ay(x{)}^4+8\mathrm{\#}\text{1}ay(x{)}^2+2a-y(x{)}^6-y(x{)}^4-1\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{48{\mathrm{\#}\text{1}}^2{a}^2-24\mathrm{\#}\text{1}ay(x{)}^2-8\mathrm{\#}\text{1}a+3y(x{)}^4+2y(x{)}^2}\mathrm{\&}])=c_1,y(x)]$$

Maple: cpu = 0.359 (sec), leaf count = 75 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{\mathit{\_}\mathit{a}}{-{\mathit{\_}\mathit{a}}^6+12{\mathit{\_}\mathit{a}}^{4}ax-48{\mathit{\_}\mathit{a}}^2{a}^2{x}^2+64a^3{x}^3-{\mathit{\_}\mathit{a}}^4+8{\mathit{\_}\mathit{a}}^{2}ax-16a^2{x}^2+2a-1}\mathrm{d}\mathit{\_}\mathit{a}+x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$