2.1178   ODE No. 1178

\[ x^3 (-\sec (x))+x^2 y''(x)+\left (x^2+2\right ) y(x)-2 x y'(x)=0 \] Mathematica : cpu = 0.0345741 (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 = 0.031 (sec), leaf count = 23


\[y \relax (x ) = x \left (\cos \relax (x ) \ln \left (\cos \relax (x )\right )+\cos \relax (x ) c_{1}+\sin \relax (x ) \left (x +c_{2}\right )\right )\]