4.400   ODE No. 1400

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x}}-{\frac {ay \left ( x \right ) }{{x}^{6}}}=0} \]

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

Mathematica: cpu = 0.050506 (sec), leaf count = 60 \[ \left \{\left \{y(x)\to c_1 x^2 e^{\frac {\sqrt {-a}}{2 x^2}}+\frac {c_2 x^2 e^{-\frac {\sqrt {-a}}{2 x^2}}}{2 \sqrt {-a}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}\sinh \left ( {\frac {1 }{2\,{x}^{2}}\sqrt {-a}} \right ) +{\it \_C2}\,{x}^{2}\cosh \left ( { \frac {1}{2\,{x}^{2}}\sqrt {-a}} \right ) \right \} \]