3.966   ODE No. 966

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-1296\frac{y\left(x\right)}{216-432xy\left(x\right)-648x^{2}y\left(x\right)+216x{\left(y\left(x\right)\right)}^2-1296y\left(x\right)+216x^3+216x^2-2376{\left(y\left(x\right)\right)}^2-1728{\left(y\left(x\right)\right)}^3+1080x{\left(y\left(x\right)\right)}^3-324x^2{\left(y\left(x\right)\right)}^3-648x^2{\left(y\left(x\right)\right)}^2-1944{\left(y\left(x\right)\right)}^4-126{\left(y\left(x\right)\right)}^{10}-315{\left(y\left(x\right)\right)}^9-8{\left(y\left(x\right)\right)}^{12}-36{\left(y\left(x\right)\right)}^{11}-846{\left(y\left(x\right)\right)}^7+72{\left(y\left(x\right)\right)}^{8}x+216{\left(y\left(x\right)\right)}^{7}x+1080{\left(y\left(x\right)\right)}^{5}x-570{\left(y\left(x\right)\right)}^8+594x{\left(y\left(x\right)\right)}^6-216x^2{\left(y\left(x\right)\right)}^4-882{\left(y\left(x\right)\right)}^6+1152x{\left(y\left(x\right)\right)}^4-612{\left(y\left(x\right)\right)}^5}=0}}$$

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

Mathematica: cpu = 0.439556 (sec), leaf count = 292 $$\text{Solve}[72\text{RootSum}[-216{\mathrm{\#}\text{1}}^3+216{\mathrm{\#}\text{1}}^{2}y(x{)}^4+324{\mathrm{\#}\text{1}}^{2}y(x{)}^3+648{\mathrm{\#}\text{1}}^{2}y(x{)}^2+648{\mathrm{\#}\text{1}}^{2}y(x)-216{\mathrm{\#}\text{1}}^2-72\mathrm{\#}\text{1}y(x{)}^8-216\mathrm{\#}\text{1}y(x{)}^7-594\mathrm{\#}\text{1}y(x{)}^6-1080\mathrm{\#}\text{1}y(x{)}^5-1152\mathrm{\#}\text{1}y(x{)}^4-1080\mathrm{\#}\text{1}y(x{)}^3-216\mathrm{\#}\text{1}y(x{)}^2+432\mathrm{\#}\text{1}y(x)+8y(x{)}^{12}+36y(x{)}^{11}+126y(x{)}^{10}+315y(x{)}^9+570y(x{)}^8+846y(x{)}^7+882y(x{)}^6+612y(x{)}^5+216y(x{)}^4-216y(x{)}^3-216y(x{)}^2-216\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{36{\mathrm{\#}\text{1}}^2-24\mathrm{\#}\text{1}y(x{)}^4-36\mathrm{\#}\text{1}y(x{)}^3-72\mathrm{\#}\text{1}y(x{)}^2-72\mathrm{\#}\text{1}y(x)+24\mathrm{\#}\text{1}+4y(x{)}^8+12y(x{)}^7+33y(x{)}^6+60y(x{)}^5+64y(x{)}^4+60y(x{)}^3+12y(x{)}^2-24y(x)}\mathrm{\&}]+\log (y(x))=c_1,y(x)]$$

Maple: cpu = 0.484 (sec), leaf count = 50 $$\{y\left(x\right)={\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{Z}-6{\int }^{x-1/3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^4-1/2{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^3-{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2-{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{({\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{a}}^2+1)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}\}$$