3.945   ODE No. 945

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{-32xy\left(x\right)-8x^3-16a{x}^2-32x+64{\left(y\left(x\right)\right)}^3+48x^2{\left(y\left(x\right)\right)}^2+96ax{\left(y\left(x\right)\right)}^2+12y\left(x\right)x^4+48y\left(x\right)a{x}^3+48a^2{x}^{2}y\left(x\right)+x^6+6x^{5}a+12a^2{x}^4+8a^3{x}^3}{64y\left(x\right)+16x^2+32ax+64}=0}}$$

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

Mathematica: cpu = 1.213154 (sec), leaf count = 213 $$\text{Solve}[x-4\text{RootSum}[{\mathrm{\#}\text{1}}^6+6{\mathrm{\#}\text{1}}^{5}a+12{\mathrm{\#}\text{1}}^4{a}^2+12{\mathrm{\#}\text{1}}^{4}y(x)+8{\mathrm{\#}\text{1}}^3{a}^3+48{\mathrm{\#}\text{1}}^{3}ay(x)+48{\mathrm{\#}\text{1}}^2{a}^{2}y(x)+8{\mathrm{\#}\text{1}}^{2}a+48{\mathrm{\#}\text{1}}^{2}y(x{)}^2+16\mathrm{\#}\text{1}{a}^2+96\mathrm{\#}\text{1}ay(x{)}^2+32ay(x)+32a+64y(x{)}^3\mathrm{\&},\frac{{\mathrm{\#}\text{1}}^2\log (x-\mathrm{\#}\text{1})+2\mathrm{\#}\text{1}a\log (x-\mathrm{\#}\text{1})+4y(x)\log (x-\mathrm{\#}\text{1})+4\log (x-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^4+12{\mathrm{\#}\text{1}}^{3}a+12{\mathrm{\#}\text{1}}^2{a}^2+24{\mathrm{\#}\text{1}}^{2}y(x)+48\mathrm{\#}\text{1}ay(x)+8a+48y(x{)}^2}\mathrm{\&}]=c_1,y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 41 $$\{y\left(x\right)=-\frac{x^2}{4}-\frac{ax}{2}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}2\frac{\mathit{\_}\mathit{a}+1}{2{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{a}a+a}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\}$$