8.87   ODE No. 1677

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+ay\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+bx=0}}$$

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

Mathematica: cpu = 46.986967 (sec), leaf count = 28 $$\text{DSolve}[ay(x)y^{\prime }(x{)}^2+bx+x^2{y}^{″}(x)=0,y(x),x]$$

Maple: cpu = 2.309 (sec), leaf count = 101 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(a{\mathit{\_}\mathit{a}}^3+b){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(2{\mathit{\_}\mathit{a}}^{2}a+1){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)a\},\{\mathit{\_}\mathit{a}=\frac{y\left(x\right)}{x},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{x}{-x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$