3.439   ODE No. 439

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

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

Mathematica: cpu = 0.034504 (sec), leaf count = 49 $$\{\{y(x)\to c_1{x}^{\frac{1}{2}(-3-i\sqrt{3})}\},\{y(x)\to c_1{x}^{\frac{1}{2}i(\sqrt{3}+3i)}\}\}$$

Maple: cpu = 0.546 (sec), leaf count = 33 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{i}{2}\sqrt{3}}{x}^{-\frac{3}{2}},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{\frac{i}{2}\sqrt{3}}{x}^{-\frac{3}{2}}\}$$