3.445   ODE No. 445

\[ \boxed { {x}^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( a{x}^{2} \left ( y \left ( x \right ) \right ) ^{3}+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ab \left ( y \left ( x \right ) \right ) ^{3}=0} \]

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

Mathematica: cpu = 0.009001 (sec), leaf count = 49 \[ \left \{\left \{y(x)\to -\frac {1}{\sqrt {2 a x-2 c_1}}\right \},\left \{y(x)\to \frac {1}{\sqrt {2 a x-2 c_1}}\right \},\left \{y(x)\to \frac {b}{x}+c_1\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\frac {1}{\sqrt {2\,ax+{\it \_C1}}}},y \left ( x \right ) =-{\frac {1}{\sqrt {2\,ax+{\it \_C1}}}},y \left ( x \right ) ={\frac {b}{x}}+{\it \_C1} \right \} \]