2.1178   ODE No. 1178

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

\[ x^3 (-\sec (x))+x^2 y''(x)+\left (x^2+2\right ) y(x)-2 x y'(x)=0 \] Mathematica : cpu = 0.0547803 (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 = 0.023 (sec), leaf count = 28

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