3.392   ODE No. 392

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

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

Mathematica: cpu = 0.255032 (sec), leaf count = 27 $$\left\{\{y(x)\to \frac{e^{\frac{c_{1}x}{2}-\frac{c_1^2}{4}}}{a}\}\right\}$$

Maple: cpu = 0.312 (sec), leaf count = 50 $$\{y\left(x\right)=\frac{1}{a}{\mathrm{e}}^{\frac{x^2}{4}},y\left(x\right)=\frac{1}{{\mathrm{e}}^{{\mathit{\_}\mathit{C}\mathit{1}}^2}{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}x}a},y\left(x\right)=\frac{{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}x}}{{\mathrm{e}}^{{\mathit{\_}\mathit{C}\mathit{1}}^2}a}\}$$