3.45   ODE No. 45

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

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

Mathematica: cpu = 0.522566 (sec), leaf count = 133 $$\text{Solve}[c_1=\sqrt[4]{{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)})}^2-1}(-\frac{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)}){}_2{F}_1(\frac{1}{2},\frac{3}{4};\frac{3}{2};{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)})}^2)}{2\sqrt[4]{1-{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)})}^2}}-\frac{ax}{b}),y(x)]$$

Maple: cpu = 0.094 (sec), leaf count = 123 $$\{\mathit{\_}\mathit{C}\mathit{1}+1\sqrt[4]{{(\frac{ax}{b}+{(\frac{b^{2}y\left(x\right)}{a}-\frac{b}{ax})}^{-1})}^2-1}{(\frac{b^{2}y\left(x\right)}{a}-\frac{b}{ax})}^{-1}\frac{1}{\sqrt{\frac{ax}{b}+{(\frac{b^{2}y\left(x\right)}{a}-\frac{b}{ax})}^{-1}}}-{\int }^{\frac{a{x}^{2}y\left(x\right)}{bxy\left(x\right)-1}}1\sqrt[4]{{\mathit{\_}\mathit{a}}^2-1}\frac{1}{\sqrt{\mathit{\_}\mathit{a}}}d\mathit{\_}\mathit{a}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$