4.191   ODE No. 1191

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

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

Mathematica: cpu = 0.008501 (sec), leaf count = 110 \[ \left \{\left \{y(x)\to \frac {2 c_2 e^{\frac {1}{2} (\log (x)-x)} \left (i \sinh \left (\frac {x}{2}\right )-\frac {2 i \cosh \left (\frac {x}{2}\right )}{x}\right )}{\sqrt {\pi } \sqrt {-i x}}+\frac {2 c_1 e^{\frac {1}{2} (\log (x)-x)} \left (\frac {2 \sinh \left (\frac {x}{2}\right )}{x}-\cosh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( x-2 \right ) }{x}}+{\frac {{\it \_C2}\,{{\rm e}^{-x}} \left ( x+2 \right ) }{x}} \right \} \]