8.172   ODE No. 1762

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

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

Mathematica: cpu = 52.685690 (sec), leaf count = 39 $$\text{DSolve}[ay(x)y^{\prime }(x)+bxy(x{)}^3+xy(x)y^{″}(x)-x{y}^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 2.215 (sec), leaf count = 106 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\frac{\mathit{\_}\mathit{a}}{{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^2},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\mathit{\_}\mathit{a}(b\mathit{\_}\mathit{a}-2a+2){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(a-1){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-\frac{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}{\mathit{\_}\mathit{a}}\},\{\mathit{\_}\mathit{a}=x^{2}y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{1}{x^2(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right))}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\frac{\mathit{\_}\mathit{a}}{{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^2}\}])\}$$