2.168   ODE No. 168

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

\[ 3 \left (x^2-4\right ) y'(x)+y(x)^2-x y(x)-3=0 \] Mathematica : cpu = 0.0906268 (sec), leaf count = 99

\[\left \{\left \{y(x)\to \frac {-2 c_1 x P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+3 c_1 P_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )-2 x Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+3 Q_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}{c_1 P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}\right \}\right \}\]

Maple : cpu = 0.191 (sec), leaf count = 140

\[ \left \{ y \left ( x \right ) =-3\,{(x+2) \left ( {\it HeunC} \left ( 0,4/3,-1/3,0,{\frac {25}{36}},4\, \left ( x+2 \right ) ^{-1} \right ) {\it \_C1}-1/3\, \left ( -x/4-1/2 \right ) ^{4/3}{\it HeunC} \left ( 0,-4/3,-1/3,0,{\frac {25}{36}},4\, \left ( x+2 \right ) ^{-1} \right ) \right ) \left ( 4\,{\it \_C1}\, \left ( x+2 \right ) \left ( x-5/4 \right ) {\it HeunC} \left ( 0,4/3,-1/3,0,{\frac {25}{36}},4\, \left ( x+2 \right ) ^{-1} \right ) - \left ( -x/4-1/2 \right ) ^{4/3} \left ( x+2 \right ) {\it HeunC} \left ( 0,-4/3,-1/3,0,{\frac {25}{36}},4\, \left ( x+2 \right ) ^{-1} \right ) +12\, \left ( {\it HeunCPrime} \left ( 0,4/3,-1/3,0,{\frac {25}{36}},4\, \left ( x+2 \right ) ^{-1} \right ) {\it \_C1}-1/3\, \left ( -x/4-1/2 \right ) ^{4/3}{\it HeunCPrime} \left ( 0,-4/3,-1/3,0,{\frac {25}{36}},4\, \left ( x+2 \right ) ^{-1} \right ) \right ) \left ( x-2 \right ) \right ) ^{-1}} \right \} \]