2.1508   ODE No. 1508

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

\[ y(x) \left (a x^3+\nu ^2-1\right )+\left (1-\nu ^2\right ) x y'(x)+x^3 y^{(3)}(x)=0 \] Mathematica : cpu = 0.980183 (sec), leaf count = 143

\[\left \{\left \{y(x)\to 3^{-\nu -1} x a^{-\nu /3} \left (a^{\frac {\nu +1}{3}} \left (c_3 a^{\nu /3} x^{\nu } \, _0F_2\left (;\frac {\nu }{3}+1,\frac {2 \nu }{3}+1;-\frac {a x^3}{27}\right )+c_1 3^{\nu } \, _0F_2\left (;1-\frac {\nu }{3},\frac {\nu }{3}+1;-\frac {a x^3}{27}\right )\right )+\sqrt [3]{a} c_2 9^{\nu } x^{-\nu } \, _0F_2\left (;1-\frac {2 \nu }{3},1-\frac {\nu }{3};-\frac {a x^3}{27}\right )\right )\right \}\right \}\]

Maple : cpu = 0.158 (sec), leaf count = 81

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,x{\mbox {$_0$F$_2$}(\ ;\,{\frac {\nu }{3}}+1,-{\frac {\nu }{3}}+1;\,-{\frac {a{x}^{3}}{27}})}+{\it \_C2}\,{x}^{-\nu +1}{\mbox {$_0$F$_2$}(\ ;\,-{\frac {\nu }{3}}+1,1-{\frac {2\,\nu }{3}};\,-{\frac {a{x}^{3}}{27}})}+{\it \_C3}\,{x}^{\nu +1}{\mbox {$_0$F$_2$}(\ ;\,{\frac {\nu }{3}}+1,{\frac {2\,\nu }{3}}+1;\,-{\frac {a{x}^{3}}{27}})} \right \} \]