3.41   ODE No. 41

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

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

Mathematica: cpu = 0.076010 (sec), leaf count = 103 \[ \text {Solve}\left [-\frac {b^2 \left (\frac {2 \tan ^{-1}\left (\frac {-2 a x y(x)-b}{b \sqrt {-\frac {4 a}{b^2}-1}}\right )}{\sqrt {-\frac {4 a}{b^2}-1}}-\log \left (\frac {a (-x) y(x) (-a x y(x)-b)-a}{a^2 x^2 y(x)^2}\right )\right )}{2 a}=c_1-\frac {b^2 \log (x)}{a},y(x)\right ] \]

Maple: cpu = 0.172 (sec), leaf count = 103 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}{{\rm e}^{{\it RootOf} \left ( 2\,\sqrt {{b}^{2}+4\,a}b{\it Artanh} \left ( {\frac {2\,a{ {\rm e}^{{\it \_Z}}}+b}{\sqrt {{b}^{2}+4\,a}}} \right ) -\ln \left ( {x }^{2} \left ( a{{\rm e}^{2\,{\it \_Z}}}+b{{\rm e}^{{\it \_Z}}}-1 \right ) \right ) {b}^{2}+2\,{\it \_C1}\,{b}^{2}+2\,{\it \_Z}\,{b}^{2} -4\,\ln \left ( {x}^{2} \left ( a{{\rm e}^{2\,{\it \_Z}}}+b{{\rm e}^{{ \it \_Z}}}-1 \right ) \right ) a+8\,{\it \_C1}\,a+8\,{\it \_Z}\,a \right ) }}} \right \} \]

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