5.29   ODE No. 1477

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

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

Mathematica: cpu = 0.170522 (sec), leaf count = 48 \[ \left \{\left \{y(x)\to \frac {c_1 e^{-x}}{x}+\frac {c_2 e^{\sqrt [3]{-1} x}}{x}+\frac {c_3 e^{-(-1)^{2/3} x}}{x}\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C1}\,{{\rm e} ^{-x}}+{\it \_C2}\,{{\rm e}^{{\frac {x}{2}}}}\sin \left ( {\frac { \sqrt {3}x}{2}} \right ) +{\it \_C3}\,{{\rm e}^{{\frac {x}{2}}}}\cos \left ( {\frac {\sqrt {3}x}{2}} \right ) \right ) } \right \} \]