5.42   ODE No. 1490

\[ \boxed { {x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {x}^{2}+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.018502 (sec), leaf count = 33 \[ \left \{\left \{y(x)\to \frac {1}{2} c_1 x^2 \, _0\tilde {F}_1\left (;2;-\frac {x^2}{4}\right )+c_2 x Y_1(x)+c_3\right \}\right \} \]

Maple: cpu = 0.063 (sec), leaf count = 18 \[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,x{{\sl J}_{1 }\left (x\right )}+{\it \_C3}\,x{{\sl Y}_{1}\left (x\right )} \right \} \]