4.1.25 \(y'(x)=y(x) \sec (x)\)

ODE
\[ y'(x)=y(x) \sec (x) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0093707 (sec), leaf count = 19

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

Maple
cpu = 0.006 (sec), leaf count = 11

\[ \left \{ y \relax (x ) ={\it \_C1}\, \left (\sec \relax (x ) +\tan \relax (x ) \right ) \right \} \] Mathematica raw input

DSolve[y'[x] == Sec[x]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> E^(2*ArcTanh[Tan[x/2]])*C[1]}}

Maple raw input

dsolve(diff(y(x),x) = y(x)*sec(x), y(x),'implicit')

Maple raw output

y(x) = _C1*(sec(x)+tan(x))