2.1497   ODE No. 1497

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

\[ 3 p (3 q+1) y'(x)-3 x (p+q) y''(x)+x^2 y^{(3)}(x)+x^2 (-y(x))=0 \] Mathematica : cpu = 0.362773 (sec), leaf count = 135

\[\left \{\left \{y(x)\to c_2 (-1)^{\frac {1}{3} (3 p+1)} 3^{-3 p-1} x^{3 p+1} \, _0F_2\left (;p+\frac {4}{3},p-q+\frac {2}{3};\frac {x^3}{27}\right )+c_3 (-1)^{\frac {1}{3} (3 q+2)} 3^{-3 q-2} x^{3 q+2} \, _0F_2\left (;q+\frac {5}{3},-p+q+\frac {4}{3};\frac {x^3}{27}\right )+c_1 \, _0F_2\left (;\frac {2}{3}-p,\frac {1}{3}-q;\frac {x^3}{27}\right )\right \}\right \}\] Maple : cpu = 0.246 (sec), leaf count = 77

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