ODE
\[ y'(x)+\tan (x)=(1-y(x)) \sec (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.363134 (sec), leaf count = 21
\[\left \{\left \{y(x)\to (x+c_1) e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 15
\[\left [y \left (x \right ) = \frac {x +\textit {\_C1}}{\sec \left (x \right )+\tan \left (x \right )}\right ]\] Mathematica raw input
DSolve[Tan[x] + y'[x] == Sec[x]*(1 - y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (x + C[1])/E^(2*ArcTanh[Tan[x/2]])}}
Maple raw input
dsolve(diff(y(x),x)+tan(x) = (1-y(x))*sec(x), y(x))
Maple raw output
[y(x) = (x+_C1)/(sec(x)+tan(x))]