3.883   ODE No. 883

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{(a^3+{\left(y\left(x\right)\right)}^4{a}^3+2{\left(y\left(x\right)\right)}^2{a}^{2}b{x}^2+a{x}^4{b}^2+{\left(y\left(x\right)\right)}^6{a}^3+3{\left(y\left(x\right)\right)}^4{a}^{2}b{x}^2+3{\left(y\left(x\right)\right)}^{2}a{b}^2{x}^4+b^3{x}^6)x}{a^{7/2}y\left(x\right)}=0}}$$

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

Mathematica: cpu = 1.403178 (sec), leaf count = 164 $$\text{Solve}[\frac{x^2}{2}-\frac{1}{2}{a}^{5/2}\text{RootSum}[{\mathrm{\#}\text{1}}^3{b}^3+3{\mathrm{\#}\text{1}}^{2}a{b}^{2}y(x{)}^2+{\mathrm{\#}\text{1}}^{2}a{b}^2+3\mathrm{\#}\text{1}{a}^{2}by(x{)}^4+2\mathrm{\#}\text{1}{a}^{2}by(x{)}^2+a^{5/2}b+a^{3}y(x{)}^6+a^{3}y(x{)}^4+a^3\mathrm{\&},\frac{\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2{b}^2+6\mathrm{\#}\text{1}aby(x{)}^2+2\mathrm{\#}\text{1}ab+3a^{2}y(x{)}^4+2a^{2}y(x{)}^2}\mathrm{\&}]=c_1,y(x)]$$

Maple: cpu = 0.592 (sec), leaf count = 595 $$\{{\int }_{\mathit{\_}\mathit{b}}^x(b^3{\mathit{\_}\mathit{a}}^6+3{\left(y\left(x\right)\right)}^{2}a{b}^2{\mathit{\_}\mathit{a}}^4+3{\left(y\left(x\right)\right)}^4{a}^{2}b{\mathit{\_}\mathit{a}}^2+{\left(y\left(x\right)\right)}^6{a}^3+a{\mathit{\_}\mathit{a}}^4{b}^2+2{\left(y\left(x\right)\right)}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+{\left(y\left(x\right)\right)}^4{a}^3+a^3)\mathit{\_}\mathit{a}{({\left(y\left(x\right)\right)}^6{a}^3+3{\left(y\left(x\right)\right)}^4{a}^{2}b{\mathit{\_}\mathit{a}}^2+3{\left(y\left(x\right)\right)}^{2}a{b}^2{\mathit{\_}\mathit{a}}^4+b^3{\mathit{\_}\mathit{a}}^6+{\left(y\left(x\right)\right)}^4{a}^3+2{\left(y\left(x\right)\right)}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{a}}^4{b}^2+a^3+a^{\frac{5}{2}}b)}^{-1}{a}^{-\frac{7}{2}}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-\mathit{\_}\mathit{f}{({\mathit{\_}\mathit{f}}^6{a}^3+3{\mathit{\_}\mathit{f}}^4{a}^{2}b{x}^2+3{\mathit{\_}\mathit{f}}^{2}a{b}^2{x}^4+b^3{x}^6+{\mathit{\_}\mathit{f}}^4{a}^3+2{\mathit{\_}\mathit{f}}^2{a}^{2}b{x}^2+a{x}^4{b}^2+a^3+a^{\frac{5}{2}}b)}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^x(6{\mathit{\_}\mathit{a}}^4\mathit{\_}\mathit{f}a{b}^2+12{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^3{a}^{2}b+6{\mathit{\_}\mathit{f}}^5{a}^3+4{\mathit{\_}\mathit{a}}^2\mathit{\_}\mathit{f}{a}^{2}b+4{\mathit{\_}\mathit{f}}^3{a}^3)\mathit{\_}\mathit{a}{({\mathit{\_}\mathit{f}}^6{a}^3+3{\mathit{\_}\mathit{f}}^4{a}^{2}b{\mathit{\_}\mathit{a}}^2+3{\mathit{\_}\mathit{f}}^{2}a{b}^2{\mathit{\_}\mathit{a}}^4+b^3{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{f}}^4{a}^3+2{\mathit{\_}\mathit{f}}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{a}}^4{b}^2+a^3+a^{\frac{5}{2}}b)}^{-1}{a}^{-\frac{7}{2}}-(b^3{\mathit{\_}\mathit{a}}^6+3{\mathit{\_}\mathit{f}}^{2}a{b}^2{\mathit{\_}\mathit{a}}^4+3{\mathit{\_}\mathit{f}}^4{a}^{2}b{\mathit{\_}\mathit{a}}^2+{\mathit{\_}\mathit{f}}^6{a}^3+a{\mathit{\_}\mathit{a}}^4{b}^2+2{\mathit{\_}\mathit{f}}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+{\mathit{\_}\mathit{f}}^4{a}^3+a^3)\mathit{\_}\mathit{a}(6{\mathit{\_}\mathit{a}}^4\mathit{\_}\mathit{f}a{b}^2+12{\mathit{\_}\mathit{a}}^2{\mathit{\_}\mathit{f}}^3{a}^{2}b+6{\mathit{\_}\mathit{f}}^5{a}^3+4{\mathit{\_}\mathit{a}}^2\mathit{\_}\mathit{f}{a}^{2}b+4{\mathit{\_}\mathit{f}}^3{a}^3){({\mathit{\_}\mathit{f}}^6{a}^3+3{\mathit{\_}\mathit{f}}^4{a}^{2}b{\mathit{\_}\mathit{a}}^2+3{\mathit{\_}\mathit{f}}^{2}a{b}^2{\mathit{\_}\mathit{a}}^4+b^3{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{f}}^4{a}^3+2{\mathit{\_}\mathit{f}}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{a}}^4{b}^2+a^3+a^{\frac{5}{2}}b)}^{-2}{a}^{-\frac{7}{2}}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$