3.445   ODE No. 445

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

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

Mathematica: cpu = 0.009001 (sec), leaf count = 49 $$\{\{y(x)\to -\frac{1}{\sqrt{2ax-2c_1}}\},\{y(x)\to \frac{1}{\sqrt{2ax-2c_1}}\},\{y(x)\to \frac{b}{x}+c_1\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 35 $$\{y\left(x\right)=\frac{1}{\sqrt{2ax+\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=-\frac{1}{\sqrt{2ax+\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{b}{x}+\mathit{\_}\mathit{C}\mathit{1}\}$$