3.912   ODE No. 912

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=2\frac{ax}{-x^{3}y\left(x\right)+2a{x}^3+2a{\left(y\left(x\right)\right)}^4{x}^3-16{\left(y\left(x\right)\right)}^2{a}^2{x}^2+32a^{3}x+2a{\left(y\left(x\right)\right)}^6{x}^3-24{\left(y\left(x\right)\right)}^4{a}^2{x}^2+96{\left(y\left(x\right)\right)}^{2}x{a}^3-128a^4}=0}}$$

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

Mathematica: cpu = 1.400178 (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 = 3.026 (sec), leaf count = 43 $$\{-\frac{y\left(x\right)}{2a}+\frac{1}{8a^2}{\int }^{{\left(y\left(x\right)\right)}^2-4\frac{a}{x}}{({\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{a}}^2+1)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$