3.967   ODE No. 967

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{x(-513-432x-594x^{2}y\left(x\right)+720x^{3}y\left(x\right)-378y\left(x\right)-864x^4-756x^3-1134x^2-540{\left(y\left(x\right)\right)}^2-216{\left(y\left(x\right)\right)}^3-972x^4{\left(y\left(x\right)\right)}^2-216x^6{\left(y\left(x\right)\right)}^2+432x^3{\left(y\left(x\right)\right)}^2-648x^2{\left(y\left(x\right)\right)}^3-1296x^2{\left(y\left(x\right)\right)}^2-288y\left(x\right)x^8+288y\left(x\right)x^7+864{\left(y\left(x\right)\right)}^2{x}^5-648{\left(y\left(x\right)\right)}^3{x}^4-144x^7+64x^9-96x^8-288y\left(x\right)x^6-216y\left(x\right)x^4+432{\left(y\left(x\right)\right)}^2{x}^7-216x^6{\left(y\left(x\right)\right)}^3+1008x^{5}y\left(x\right)-456x^6-576x^5)}{216{(x^2+1)}^4}=0}}$$

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

Mathematica: cpu = 0.128516 (sec), leaf count = 151 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{3xy(x)}{x^2+1}+\frac{-4x^4+2x^3+5x}{2{(x^2+1)}^2}}{\sqrt[3]{29}\sqrt[3]{\frac{x^3}{{(x^2+1)}^3}}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{{29}^{2/3}{\left(\frac{x^3}{{(x^2+1)}^3}\right)}^{2/3}{(x^2+1)}^2\log (x^2+1)}{18x^2},y(x)]$$

Maple: cpu = 0.062 (sec), leaf count = 90 $$\{y\left(x\right)=\frac{58\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-162{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+\ln (x^2+1)+6\mathit{\_}\mathit{C}\mathit{1})x^2+12x^3-6x^2+58\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-162{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+\ln (x^2+1)+6\mathit{\_}\mathit{C}\mathit{1})-15}{18x^2+18}\}$$