2.445   ODE No. 445

\[ y'(x) \left (a x^2 y(x)^3+b\right )+a b y(x)^3+x^2 y'(x)^2=0 \] Mathematica : cpu = 0.0628687 (sec), leaf count = 49


\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {2 a x-2 c_1}}\right \},\left \{y(x)\to \frac {1}{\sqrt {2 a x-2 c_1}}\right \},\left \{y(x)\to \frac {b}{x}+c_1\right \}\right \}\] Maple : cpu = 0.023 (sec), leaf count = 35


\[y \relax (x ) = \frac {1}{\sqrt {2 a x +c_{1}}}\]