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 = 0.851903 (sec), leaf count = 136

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

Maple : cpu = 0.153 (sec), leaf count = 81

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