2.1497   ODE No. 1497

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

\[ -3 x (p+q) y''(x)+3 p (3 q+1) y'(x)+x^2 y^{(3)}(x)+x^2 (-y(x))=0 \] Mathematica : cpu = 0.539638 (sec), leaf count = 127

\[\left \{\left \{y(x)\to c_1 \, _0F_2\left (;\frac {2}{3}-p,\frac {1}{3}-q;\frac {x^3}{27}\right )+c_2 (-1)^{p+\frac {1}{3}} 3^{-3 p-1} x^{3 p+1} \, _0F_2\left (;p+\frac {4}{3},p-q+\frac {2}{3};\frac {x^3}{27}\right )+c_3 (-1)^{q+\frac {2}{3}} 3^{-3 q-2} x^{3 q+2} \, _0F_2\left (;q+\frac {5}{3},-p+q+\frac {4}{3};\frac {x^3}{27}\right )\right \}\right \}\]

Maple : cpu = 0.284 (sec), leaf count = 77

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_0$F$_2$}(\ ;\,-p+{\frac {2}{3}},-q+{\frac {1}{3}};\,{\frac {{x}^{3}}{27}})}+{\it \_C2}\,{x}^{3\,p+1}{\mbox {$_0$F$_2$}(\ ;\,p+{\frac {4}{3}},-q+{\frac {2}{3}}+p;\,{\frac {{x}^{3}}{27}})}+{\it \_C3}\,{x}^{3\,q+2}{\mbox {$_0$F$_2$}(\ ;\,q+{\frac {5}{3}},q+{\frac {4}{3}}-p;\,{\frac {{x}^{3}}{27}})} \right \} \]