2.964   ODE No. 964

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

$$y^{\prime }(x)=-\frac{8(a-1)(a+1)x}{a^8{x}^6-4a^6{x}^6-3a^6{x}^{4}y(x{)}^2-2a^6{x}^4+6a^4{x}^6+9a^4{x}^{4}y(x{)}^2+6a^4{x}^4+3a^4{x}^{2}y(x{)}^4+4a^4{x}^{2}y(x{)}^2-4a^2{x}^6-9a^2{x}^{4}y(x{)}^2-6a^2{x}^4-6a^2{x}^{2}y(x{)}^4-8a^2{x}^{2}y(x{)}^2-a^{2}y(x{)}^6-2a^{2}y(x{)}^4-8a^2+x^6+3x^{4}y(x{)}^2+2x^4+3x^{2}y(x{)}^4+4x^{2}y(x{)}^2+y(x{)}^6+2y(x{)}^4-8y(x)+8}$$ ✓ Mathematica : cpu = 5.72073 (sec), leaf count = 247

$$\text{Solve}[(a^2-1)c_1=\frac{4\text{RootSum}[-{\mathrm{\#}\text{1}}^3{a}^6+3{\mathrm{\#}\text{1}}^3{a}^4-3{\mathrm{\#}\text{1}}^3{a}^2+{\mathrm{\#}\text{1}}^3+3{\mathrm{\#}\text{1}}^2{a}^{4}y(x{)}^2+2{\mathrm{\#}\text{1}}^2{a}^4-6{\mathrm{\#}\text{1}}^2{a}^{2}y(x{)}^2-4{\mathrm{\#}\text{1}}^2{a}^2+3{\mathrm{\#}\text{1}}^{2}y(x{)}^2+2{\mathrm{\#}\text{1}}^2-3\mathrm{\#}\text{1}{a}^{2}y(x{)}^4-4\mathrm{\#}\text{1}{a}^{2}y(x{)}^2+3\mathrm{\#}\text{1}y(x{)}^4+4\mathrm{\#}\text{1}y(x{)}^2+y(x{)}^6+2y(x{)}^4+8\mathrm{\&},\frac{\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2{a}^4-6{\mathrm{\#}\text{1}}^2{a}^2+3{\mathrm{\#}\text{1}}^2-6\mathrm{\#}\text{1}{a}^{2}y(x{)}^2-4\mathrm{\#}\text{1}{a}^2+6\mathrm{\#}\text{1}y(x{)}^2+4\mathrm{\#}\text{1}+3y(x{)}^4+4y(x{)}^2}\mathrm{\&}]}{a^2-1}+y(x),y(x)]$$

✓ Maple : cpu = 4.441 (sec), leaf count = 80

$$\{\frac{y\left(x\right)}{(a-1)(a+1)}+4\frac{1}{a^4-2a^2+1}\sum _{\mathit{\_}\mathit{R}=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^3+2{\mathit{\_}\mathit{Z}}^2+8)}\frac{\ln (-a^2{x}^2+x^2+{\left(y\left(x\right)\right)}^2-\mathit{\_}\mathit{R})}{3{\mathit{\_}\mathit{R}}^2+4\mathit{\_}\mathit{R}}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$