2.967   ODE No. 967

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

$$y^{\prime }(x)=-\frac{x(64x^9-288x^{8}y(x)-96x^8+432x^{7}y(x{)}^2+288x^{7}y(x)-144x^7-216x^{6}y(x{)}^3-216x^{6}y(x{)}^2-288x^{6}y(x)-456x^6+864x^{5}y(x{)}^2+1008x^{5}y(x)-576x^5-648x^{4}y(x{)}^3-972x^{4}y(x{)}^2-216x^{4}y(x)-864x^4+432x^{3}y(x{)}^2+720x^{3}y(x)-756x^3-648x^{2}y(x{)}^3-1296x^{2}y(x{)}^2-594x^{2}y(x)-1134x^2-216y(x{)}^3-540y(x{)}^2-378y(x)-432x-513)}{216{(x^2+1)}^4}$$ ✓ Mathematica : cpu = 0.135984 (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 = 0.089 (sec), leaf count = 90

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