3.964   ODE No. 964

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-8\frac{x(a-1)(a+1)}{8-8y\left(x\right)+2x^4+3x^4{\left(y\left(x\right)\right)}^2+4x^2{\left(y\left(x\right)\right)}^2+2{\left(y\left(x\right)\right)}^4+3a^4{\left(y\left(x\right)\right)}^4{x}^2-3a^6{\left(y\left(x\right)\right)}^2{x}^4+9{\left(y\left(x\right)\right)}^2{a}^4{x}^4-9{\left(y\left(x\right)\right)}^2{a}^2{x}^4-a^2{\left(y\left(x\right)\right)}^6+a^8{x}^6-4a^6{x}^6+6a^4{x}^6-2a^2{\left(y\left(x\right)\right)}^4-2a^6{x}^4+6a^4{x}^4-6a^2{x}^4-4a^2{x}^6-6{\left(y\left(x\right)\right)}^4{a}^2{x}^2+4a^4{\left(y\left(x\right)\right)}^2{x}^2-8{\left(y\left(x\right)\right)}^2{a}^2{x}^2+3x^2{\left(y\left(x\right)\right)}^4+x^6+{\left(y\left(x\right)\right)}^6-8a^2}=0}}$$

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

Mathematica: cpu = 4.810111 (sec), leaf count = 264 $$\text{Solve}[\frac{y(x)}{(a-1)(a+1)}-\frac{8\text{RootSum}[-{\mathrm{\#}\text{1}}^3{a}^6+3{\mathrm{\#}\text{1}}^3{a}^4-3{\mathrm{\#}\text{1}}^3{a}^2+{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^2{a}^{4}y(x{)}^2+2{\mathrm{\#}\text{1}}^2{a}^4-6{\mathrm{\#}\text{1}}^2{a}^{2}y(x{)}^2-4{\mathrm{\#}\text{1}}^2{a}^2+3{\mathrm{\#}\text{1}}^{2}y(x{)}^2+2{\mathrm{\#}\text{1}}^2-3\mathrm{\#}\text{1}{a}^{2}y(x{)}^4-4\mathrm{\#}\text{1}{a}^{2}y(x{)}^2+3\mathrm{\#}\text{1}y(x{)}^4+4\mathrm{\#}\text{1}y(x{)}^2+y(x{)}^6+2y(x{)}^4+8\mathrm{\&},\frac{\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2{a}^4-6{\mathrm{\#}\text{1}}^2{a}^2+3{\mathrm{\#}\text{1}}^2-6\mathrm{\#}\text{1}{a}^{2}y(x{)}^2-4\mathrm{\#}\text{1}{a}^2+6\mathrm{\#}\text{1}y(x{)}^2+4\mathrm{\#}\text{1}+3y(x{)}^4+4y(x{)}^2}\mathrm{\&}]}{(a-1)(a+1)(2-2a^2)}=c_1,y(x)]$$

Maple: cpu = 2.012 (sec), leaf count = 80 $$\{\frac{y\left(x\right)}{(a-1)(a+1)}+4\frac{1}{a^4-2a^2+1}\sum _{\mathit{\_}\mathit{R}=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^3+2{\mathit{\_}\mathit{Z}}^2+8)}\frac{\ln (-a^2{x}^2+x^2+{\left(y\left(x\right)\right)}^2-\mathit{\_}\mathit{R})}{3{\mathit{\_}\mathit{R}}^2+4\mathit{\_}\mathit{R}}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$