2.196   ODE No. 196

\[ \cos (x) y'(x)+y(x)+(\sin (x)+1) \cos (x)=0 \] Mathematica : cpu = 0.21876 (sec), leaf count = 53


\[\left \{\left \{y(x)\to e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\sin (x)+4 \log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )\right )+c_1 e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )}\right \}\right \}\] Maple : cpu = 0.153 (sec), leaf count = 29


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