2.1455   ODE No. 1455

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

\[ x (a+b-1) y'(x)-a b y(x)+x^2 \left (-y''(x)\right )+y^{(3)}(x)=0 \] Mathematica : cpu = 0.0198855 (sec), leaf count = 127

\[\left \{\left \{y(x)\to \left (-\frac {1}{3}\right )^{2/3} c_3 x^2 \, _2F_2\left (\frac {2}{3}-\frac {a}{3},\frac {2}{3}-\frac {b}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{3}\right )+\sqrt [3]{-\frac {1}{3}} c_2 x \, _2F_2\left (\frac {1}{3}-\frac {a}{3},\frac {1}{3}-\frac {b}{3};\frac {2}{3},\frac {4}{3};\frac {x^3}{3}\right )+c_1 \, _2F_2\left (-\frac {a}{3},-\frac {b}{3};\frac {1}{3},\frac {2}{3};\frac {x^3}{3}\right )\right \}\right \}\] Maple : cpu = 0.333 (sec), leaf count = 71

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