4.342   ODE No. 1342

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {ay \left ( x \right ) }{{x}^{4}}}=0} \]

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

Mathematica: cpu = 0.041505 (sec), leaf count = 51 \[ \left \{\left \{y(x)\to c_1 x e^{\frac {\sqrt {-a}}{x}}+\frac {c_2 x e^{-\frac {\sqrt {-a}}{x}}}{2 \sqrt {-a}}\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x\sinh \left ( {\frac {1}{x} \sqrt {-a}} \right ) +{\it \_C2}\,x\cosh \left ( {\frac {1}{x}\sqrt {-a} } \right ) \right \} \]