2.912   ODE No. 912

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

$$y^{\prime }(x)=\frac{2ax}{-128a^4+96a^{3}xy(x{)}^2+32a^{3}x-24a^2{x}^{2}y(x{)}^4-16a^2{x}^{2}y(x{)}^2+2a{x}^{3}y(x{)}^6+2a{x}^{3}y(x{)}^4+2a{x}^3-x^{3}y(x)}$$ ✓ Mathematica : cpu = 1.56878 (sec), leaf count = 205

$$\text{Solve}[-\text{RootSum}[-{\mathrm{\#}\text{1}}^{3}y(x{)}^6-{\mathrm{\#}\text{1}}^{3}y(x{)}^4-{\mathrm{\#}\text{1}}^3+12{\mathrm{\#}\text{1}}^{2}ay(x{)}^4+8{\mathrm{\#}\text{1}}^{2}ay(x{)}^2-48\mathrm{\#}\text{1}{a}^{2}y(x{)}^2-16\mathrm{\#}\text{1}{a}^2+64a^3\mathrm{\&},\frac{\mathrm{\#}\text{1}\log (x-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^{2}y(x{)}^6+3{\mathrm{\#}\text{1}}^{2}y(x{)}^4+3{\mathrm{\#}\text{1}}^2-24\mathrm{\#}\text{1}ay(x{)}^4-16\mathrm{\#}\text{1}ay(x{)}^2+48a^{2}y(x{)}^2+16a^2}\mathrm{\&}]-\frac{\text{RootSum}[248{\mathrm{\#}\text{1}}^3+2\mathrm{\#}\text{1}-1\mathrm{\&},\mathrm{\#}\text{1}\log (248{\mathrm{\#}\text{1}}^2+186\mathrm{\#}\text{1}+29y(x{)}^2+11)\mathrm{\&}]-2ay(x)}{2a}=c_1,y(x)]$$

✓ Maple : cpu = 4.497 (sec), leaf count = 43

$$\{-\frac{y\left(x\right)}{2a}+\frac{1}{8a^2}{\int }^{{\left(y\left(x\right)\right)}^2-4\frac{a}{x}}{({\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{a}}^2+1)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$