8.94   ODE No. 1684

$$\boxed{{\displaystyle 2x^3\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+x^2(9+2xy\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+b+xy\left(x\right)(a+3xy\left(x\right)-2x^2{\left(y\left(x\right)\right)}^2)=0}}$$

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

Mathematica: cpu = 53.614308 (sec), leaf count = 52 $$\text{DSolve}[xy(x)(a-2x^{2}y(x{)}^2+3xy(x))+b+2x^3{y}^{″}(x)+x^2(2xy(x)+9)y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 1.810 (sec), leaf count = 108 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(-{\mathit{\_}\mathit{a}}^3+\frac{{\mathit{\_}\mathit{a}}^2}{2}+\frac{a\mathit{\_}\mathit{a}}{2}-\frac{5\mathit{\_}\mathit{a}}{2}+\frac{b}{2}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(-\mathit{\_}\mathit{a}-\frac{3}{2}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=xy\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{1}{x(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right))}\},\{x={\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^{-1},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$