2.392   ODE No. 392

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

$$y(x{)}^2\log (ay(x))-xy(x)y^{\prime }(x)+y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.197263 (sec), leaf count = 27

$$\left\{\{y(x)\to \frac{e^{\frac{c_{1}x}{2}-\frac{c_1{}^2}{4}}}{a}\}\right\}$$ ✓ Maple : cpu = 1.759 (sec), leaf count = 50

$$\{y\left(x\right)=\frac{1}{a}{\mathrm{e}}^{\frac{x^2}{4}},y\left(x\right)=\frac{1}{{\mathrm{e}}^{{\mathit{\_}\mathit{C}\mathit{1}}^2}{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}x}a},y\left(x\right)=\frac{{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}x}}{{\mathrm{e}}^{{\mathit{\_}\mathit{C}\mathit{1}}^2}a}\}$$