2.883   ODE No. 883

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

$$y^{\prime }(x)=\frac{x(3a^{2}b{x}^{2}y(x{)}^4+2a^{2}b{x}^{2}y(x{)}^2+a^{3}y(x{)}^6+a^{3}y(x{)}^4+a^3+3a{b}^2{x}^{4}y(x{)}^2+a{b}^2{x}^4+b^3{x}^6)}{a^{7/2}y(x)}$$ ✓ Mathematica : cpu = 1.13261 (sec), leaf count = 164

$$\text{Solve}[\frac{x^2}{2}-\frac{1}{2}{a}^{5/2}\text{RootSum}[3{\mathrm{\#}\text{1}}^{2}a{b}^{2}y(x{)}^2+{\mathrm{\#}\text{1}}^{2}a{b}^2+{\mathrm{\#}\text{1}}^3{b}^3+3\mathrm{\#}\text{1}{a}^{2}by(x{)}^4+2\mathrm{\#}\text{1}{a}^{2}by(x{)}^2+a^{5/2}b+a^{3}y(x{)}^6+a^{3}y(x{)}^4+a^3\mathrm{\&},\frac{\log (x^2-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^2{b}^2+6\mathrm{\#}\text{1}aby(x{)}^2+2\mathrm{\#}\text{1}ab+3a^{2}y(x{)}^4+2a^{2}y(x{)}^2}\mathrm{\&}]=c_1,y(x)]$$ ✓ Maple : cpu = 1.094 (sec), leaf count = 352

$$\{{\int }_{\mathit{\_}\mathit{b}}^x(b^3{\mathit{\_}\mathit{a}}^6+3a{b}^2{\mathit{\_}\mathit{a}}^4{\left(y\left(x\right)\right)}^2+3a^{2}b{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^4+{\left(y\left(x\right)\right)}^6{a}^3+a{\mathit{\_}\mathit{a}}^4{b}^2+2{\left(y\left(x\right)\right)}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+{\left(y\left(x\right)\right)}^4{a}^3+a^3)\mathit{\_}\mathit{a}{({\left(y\left(x\right)\right)}^6{a}^3+3a^{2}b{\mathit{\_}\mathit{a}}^2{\left(y\left(x\right)\right)}^4+3a{b}^2{\mathit{\_}\mathit{a}}^4{\left(y\left(x\right)\right)}^2+b^3{\mathit{\_}\mathit{a}}^6+{\left(y\left(x\right)\right)}^4{a}^3+2{\left(y\left(x\right)\right)}^2{a}^{2}b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{a}}^4{b}^2+a^3+a^{\frac{5}{2}}b)}^{-1}{a}^{-\frac{7}{2}}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-\mathit{\_}\mathit{f}{(a^3{\mathit{\_}\mathit{f}}^6+3a^{2}b{x}^2{\mathit{\_}\mathit{f}}^4+3a{b}^2{x}^4{\mathit{\_}\mathit{f}}^2+b^3{x}^6+{\mathit{\_}\mathit{f}}^4{a}^3+2{\mathit{\_}\mathit{f}}^2{a}^{2}b{x}^2+a{x}^4{b}^2+a^3+a^{\frac{5}{2}}b)}^{-1}-{\int }_{\mathit{\_}\mathit{b}}^{x}6\frac{(b{\mathit{\_}\mathit{a}}^2+a{\mathit{\_}\mathit{f}}^2)\mathit{\_}\mathit{f}\mathit{\_}\mathit{a}(a{\mathit{\_}\mathit{f}}^2+b{\mathit{\_}\mathit{a}}^2+2/3a)b}{{(a^{5/2}b+({\mathit{\_}\mathit{f}}^6+{\mathit{\_}\mathit{f}}^4+1)a^3+3{\mathit{\_}\mathit{f}}^2{\mathit{\_}\mathit{a}}^2({\mathit{\_}\mathit{f}}^2+2/3)b{a}^2+3({\mathit{\_}\mathit{f}}^2+1/3){\mathit{\_}\mathit{a}}^4{b}^{2}a+b^3{\mathit{\_}\mathit{a}}^6)}^2}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$