8.90   ODE No. 1680

$$\boxed{{\displaystyle 4x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-x^4{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+4y\left(x\right)=0}}$$

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

Mathematica: cpu = 10.873881 (sec), leaf count = 31 $$\text{DSolve}[x^4(-y^{\prime }(x{)}^2)+4x^2{y}^{″}(x)+4y(x)=0,y(x),x]$$

Maple: cpu = 1.092 (sec), leaf count = 103 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\frac{\mathit{\_}\mathit{a}}{{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^2},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(-{\mathit{\_}\mathit{a}}^2+7\mathit{\_}\mathit{a}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(\mathit{\_}\mathit{a}-5){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-\frac{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}{4}\},\{\mathit{\_}\mathit{a}=x^{2}y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{1}{x^2(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right))}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\frac{\mathit{\_}\mathit{a}}{{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^2}\}])\}$$