4.1.27 \(y'(x)=y(x) \tan (x)\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0119539 (sec), leaf count = 10

\[\left \{\left \{y(x)\to c_1 \sec (x)\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 10

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}}{\cos \relax (x ) }} \right \} \] Mathematica raw input

DSolve[y'[x] == Tan[x]*y[x],y[x],x]

Mathematica raw output

{{y[x] -> C[1]*Sec[x]}}

Maple raw input

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

Maple raw output

y(x) = _C1/cos(x)