3.741   ODE No. 741

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{(a{\left(y\left(x\right)\right)}^2+b{x}^2)}^{3}x}{a^{5/2}(a{\left(y\left(x\right)\right)}^2+b{x}^2+a)y\left(x\right)}=0}}$$

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

Mathematica: cpu = 3.705971 (sec), leaf count = 175 $$\text{Solve}[\frac{1}{2}(x^2-a^{3/2}\text{RootSum}[{\mathrm{\#}\text{1}}^3{b}^3+3{\mathrm{\#}\text{1}}^{2}a{b}^{2}y(x{)}^2+\mathrm{\#}\text{1}{a}^{3/2}{b}^2+3\mathrm{\#}\text{1}{a}^{2}by(x{)}^4+a^{5/2}by(x{)}^2+a^{5/2}b+a^{3}y(x{)}^6\mathrm{\&},\frac{ay(x{)}^2\log (x^2-\mathrm{\#}\text{1})+a\log (x^2-\mathrm{\#}\text{1})+\mathrm{\#}\text{1}b\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2{b}^2+6\mathrm{\#}\text{1}aby(x{)}^2+a^{3/2}b+3a^{2}y(x{)}^4}\mathrm{\&}])=c_1,y(x)]$$

Maple: cpu = 0.749 (sec), leaf count = 400 $$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{{(b{\mathit{\_}\mathit{a}}^2+a{\left(y\left(x\right)\right)}^2)}^3\mathit{\_}\mathit{a}}{a^3}{({\left(y\left(x\right)\right)}^6{a}^3+3a^{2}b{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^4+3a{b}^2{\mathit{\_}\mathit{a}}^4{\left(y\left(x\right)\right)}^2+b^3{\mathit{\_}\mathit{a}}^6+a^{\frac{5}{2}}b{\left(y\left(x\right)\right)}^2+a^{\frac{3}{2}}{b}^2{\mathit{\_}\mathit{a}}^2+a^{\frac{5}{2}}b)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-(a{\mathit{\_}\mathit{f}}^2+b{x}^2+a)\mathit{\_}\mathit{f}\frac{1}{\sqrt{a}}{(a^3{\mathit{\_}\mathit{f}}^6+3a^{2}b{x}^2{\mathit{\_}\mathit{f}}^4+3a{b}^2{x}^4{\mathit{\_}\mathit{f}}^2+b^3{x}^6+a^{\frac{5}{2}}b{\mathit{\_}\mathit{f}}^2+a^{\frac{3}{2}}{b}^2{x}^2+a^{\frac{5}{2}}b)}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^x-\frac{{(b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{f}}^2)}^3\mathit{\_}\mathit{a}}{a^3}(6a^3{\mathit{\_}\mathit{f}}^5+12a^{2}b{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^3+6a{b}^2{\mathit{\_}\mathit{a}}^4\mathit{\_}\mathit{f}+2a^{5/2}b\mathit{\_}\mathit{f}){(a^3{\mathit{\_}\mathit{f}}^6+3a^{2}b{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^4+3a{b}^2{\mathit{\_}\mathit{a}}^4{\mathit{\_}\mathit{f}}^2+b^3{\mathit{\_}\mathit{a}}^6+a^{\frac{5}{2}}b{\mathit{\_}\mathit{f}}^2+a^{\frac{3}{2}}{b}^2{\mathit{\_}\mathit{a}}^2+a^{\frac{5}{2}}b)}^{-2}+6\frac{{(b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{f}}^2)}^2\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}}{a^2(a^3{\mathit{\_}\mathit{f}}^6+3a^{2}b{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^4+3a{b}^2{\mathit{\_}\mathit{a}}^4{\mathit{\_}\mathit{f}}^2+b^3{\mathit{\_}\mathit{a}}^6+a^{5/2}b{\mathit{\_}\mathit{f}}^2+a^{3/2}{b}^2{\mathit{\_}\mathit{a}}^2+a^{5/2}b)}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$