2.1178   ODE No. 1178

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

\[ x^2 y''(x)+\left (x^2+2\right ) y(x)+x^3 (-\sec (x))-2 x y'(x)=0 \] Mathematica : cpu = 0.0384999 (sec), leaf count = 74

\[\left \{\left \{y(x)\to \frac {1}{2} e^{-i x} x \left (e^{2 i x} \log \left (1+e^{-2 i x}\right )+\log \left (1+e^{2 i x}\right )\right )+c_1 e^{-i x} x-\frac {1}{2} i c_2 e^{i x} x\right \}\right \}\] Maple : cpu = 0.054 (sec), leaf count = 23

\[ \left \{ y \left ( x \right ) =x \left ( \cos \left ( x \right ) \ln \left ( \cos \left ( x \right ) \right ) +\cos \left ( x \right ) {\it \_C1}+\sin \left ( x \right ) \left ( x+{\it \_C2} \right ) \right ) \right \} \]