3.169   ODE No. 169

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

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

Mathematica: cpu = 2.095766 (sec), leaf count = 149 $$\text{Solve}[-\frac{c}{\sqrt{-a(ax+b{)}^2}}=\frac{2\exp \left(\frac{1}{2}{(-\frac{c}{\sqrt{-a(ax+b{)}^2}}-\frac{\sqrt{-a(ax+b{)}^2}}{y(x)(-ax-b)})}^2\right)}{\sqrt{2\pi }\text{erfi}\left(\frac{-\frac{c}{\sqrt{-a(ax+b{)}^2}}-\frac{\sqrt{-a(ax+b{)}^2}}{y(x)(-ax-b)}}{\sqrt{2}}\right)+2c_1},y(x)]$$

Maple: cpu = 0.141 (sec), leaf count = 153 $$\{\mathit{\_}\mathit{C}\mathit{1}+(x+\frac{b}{a}+\frac{c\sqrt{\pi }\sqrt{2}}{2}\mathit{E}\mathit{r}\mathit{f}\left(\frac{\sqrt{2}(a^{2}x+ab+cy\left(x\right))}{2(ax+b)y\left(x\right)}\frac{1}{\sqrt{a}}\right){\mathrm{e}}^{\frac{{(a^{2}x+ab+cy\left(x\right))}^2}{2{\left(y\left(x\right)\right)}^2{(ax+b)}^{2}a}}{a}^{-\frac{3}{2}}){\mathrm{e}}^{-\frac{(a^{2}x+axy\left(x\right)+ab+by\left(x\right)+cy\left(x\right))(a^{2}x-axy\left(x\right)+ab-by\left(x\right)+cy\left(x\right))}{2{\left(y\left(x\right)\right)}^2{(ax+b)}^{2}a}}=0\}$$