ODE
\[ y'(x)=y(x) \tan (x)+\cos (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0196748 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\left (2 c_1+x\right ) \sec (x)+\sin (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\frac {\sin \left ( 2\,x \right ) +2\,x+4\,{\it \_C1}}{4\,\cos \left ( x \right ) }} \right \} \] Mathematica raw input
DSolve[y'[x] == Cos[x] + Tan[x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> ((x + 2*C[1])*Sec[x] + Sin[x])/2}}
Maple raw input
dsolve(diff(y(x),x) = cos(x)+y(x)*tan(x), y(x),'implicit')
Maple raw output
y(x) = 1/4*(sin(2*x)+2*x+4*_C1)/cos(x)