4.1.28 \(y'(x)=y(x) \tan (x)+\cos (x)\)

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

\[ \left \{ y \relax (x ) ={\frac {\sin \left (2\,x \right ) +2\,x+4\,{\it \_C1}}{4\,\cos \relax (x ) }} \right \} \] 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)