5.64   ODE No. 1512

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

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

Mathematica: cpu = 0.038005 (sec), leaf count = 29 \[ \left \{\left \{y(x)\to -\frac {c_1 x^{-a}}{a}+\frac {c_2 x^a}{a}+c_3\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 18 \[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,{x}^{-a}+{\it \_C3 }\,{x}^{a} \right \} \]