2.445   ODE No. 445

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

\[ y'(x) \left (a x^2 y(x)^3+b\right )+a b y(x)^3+x^2 y'(x)^2=0 \] Mathematica : cpu = 0.070667 (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 = 0.018 (sec), leaf count = 35

\[\left \{y \left (x \right ) = \frac {1}{\sqrt {2 a x +c_{1}}}, y \left (x \right ) = -\frac {1}{\sqrt {2 a x +c_{1}}}, y \left (x \right ) = c_{1}+\frac {b}{x}\right \}\]