2.196   ODE No. 196

\[ \cos (x) y'(x)+y(x)+(\sin (x)+1) \cos (x)=0 \]

✓ Mathematica : cpu = 0.294041 (sec), leaf count = 53

DSolve[Cos[x]*(1 + Sin[x]) + y[x] + Cos[x]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\sin (x)+4 \log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )\right )+c_1 e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )}\right \}\right \}\]

✓ Maple : cpu = 0.053 (sec), leaf count = 29

dsolve(cos(x)*diff(y(x),x)+y(x)+(1+sin(x))*cos(x) = 0,y(x))
 

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