2.386   ODE No. 386

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

$$a{x}^3{y}^{\prime }(x)-2a{x}^{2}y(x)+y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.171979 (sec), leaf count = 119

$$\{\{y(x)\to \frac{1}{2}(\cosh (2c_1)+\sinh (2c_1))(-\sqrt{2}\sqrt{a}{x}^2+2\cosh (2c_1)+2\sinh (2c_1))\},\{y(x)\to \frac{\sqrt{a}{x}^2\cosh (2c_1)}{\sqrt{2}}+\frac{\sqrt{a}{x}^2\sinh (2c_1)}{\sqrt{2}}+{\cosh }^2(2c_1)+{\sinh }^2(2c_1)+2\sinh (2c_1)\cosh (2c_1)\}\}$$ ✓ Maple : cpu = 0.743 (sec), leaf count = 27

$$\{y\left(x\right)=-\frac{a{x}^4}{8},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^2+2\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{a}\}$$