4.178   ODE No. 1178

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

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

Mathematica: cpu = 0.052507 (sec), leaf count = 74 \[ \left \{\left \{y(x)\to c_1 e^{-i x} x-\frac {1}{2} i c_2 e^{i x} x+\frac {1}{2} e^{-i x} x \left (e^{2 i x} \log \left (1+e^{-2 i x}\right )+\log \left (1+e^{2 i x}\right )\right )\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 28 \[ \left \{ y \left ( x \right ) =x\sin \left ( x \right ) {\it \_C2}+\cos \left ( x \right ) x{\it \_C1}+x \left ( x\sin \left ( x \right ) +\ln \left ( \cos \left ( x \right ) \right ) \cos \left ( x \right ) \right ) \right \} \]