2.741   ODE No. 741

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

$$y^{\prime }(x)=\frac{x{(ay(x{)}^2+b{x}^2)}^3}{a^{5/2}y(x)(ay(x{)}^2+a+b{x}^2)}$$ ✓ Mathematica : cpu = 2.10914 (sec), leaf count = 175

$$\text{Solve}[\frac{1}{2}(x^2-a^{3/2}\text{RootSum}[3{\mathrm{\#}\text{1}}^{2}a{b}^{2}y(x{)}^2+{\mathrm{\#}\text{1}}^3{b}^3+\mathrm{\#}\text{1}{a}^{3/2}{b}^2+3\mathrm{\#}\text{1}{a}^{2}by(x{)}^4+a^{5/2}by(x{)}^2+a^{5/2}b+a^{3}y(x{)}^6\mathrm{\&},\frac{ay(x{)}^2\log (x^2-\mathrm{\#}\text{1})+a\log (x^2-\mathrm{\#}\text{1})+\mathrm{\#}\text{1}b\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2{b}^2+6\mathrm{\#}\text{1}aby(x{)}^2+a^{3/2}b+3a^{2}y(x{)}^4}\mathrm{\&}])=c_1,y(x)]$$ ✓ Maple : cpu = 1.548 (sec), leaf count = 246

$$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{{(b{\mathit{\_}\mathit{a}}^2+a{\left(y\left(x\right)\right)}^2)}^3\mathit{\_}\mathit{a}}{a^3}{(b({\left(y\left(x\right)\right)}^2+1)a^{\frac{5}{2}}+a^{\frac{3}{2}}{b}^2{\mathit{\_}\mathit{a}}^2+{(b{\mathit{\_}\mathit{a}}^2+a{\left(y\left(x\right)\right)}^2)}^3)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}(((-{\mathit{\_}\mathit{f}}^2-1)b{a}^{\frac{5}{2}}-a^{\frac{3}{2}}{b}^2{x}^2-{(a{\mathit{\_}\mathit{f}}^2+b{x}^2)}^3){\int }_{\mathit{\_}\mathit{b}}^{x}4\frac{b{(b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{f}}^2)}^2\mathit{\_}\mathit{a}\mathit{\_}\mathit{f}(a{\mathit{\_}\mathit{f}}^2+b{\mathit{\_}\mathit{a}}^2+3/2a)}{\sqrt{a}{(b({\mathit{\_}\mathit{f}}^2+1)a^{5/2}+a^{3/2}{b}^2{\mathit{\_}\mathit{a}}^2+{(b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{f}}^2)}^3)}^2}\mathrm{d}\mathit{\_}\mathit{a}-(a{\mathit{\_}\mathit{f}}^2+b{x}^2+a)\mathit{\_}\mathit{f}\frac{1}{\sqrt{a}}){(b({\mathit{\_}\mathit{f}}^2+1)a^{\frac{5}{2}}+a^{\frac{3}{2}}{b}^2{x}^2+{(a{\mathit{\_}\mathit{f}}^2+b{x}^2)}^3)}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$