3.386   ODE No. 386

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

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

Mathematica: cpu = 0.204526 (sec), leaf count = 56 $$\{\{y(x)\to 2a{e}^{2c_1}(4e^{2c_1}+x^2)\},\{y(x)\to \frac{e^{2c_1}(e^{2c_1}-2a{x}^2)}{8a}\}\}$$

Maple: cpu = 0.655 (sec), leaf count = 27 $$\{y\left(x\right)=-\frac{a{x}^4}{8},y\left(x\right)=x^2\mathit{\_}\mathit{C}\mathit{1}+2\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{a}\}$$