\[ \left \{x'(t)=x(t) \cos (t),y'(t)=x(t) e^{-\sin (t)}\right \} \] ✓ Mathematica : cpu = 0.0202381 (sec), leaf count = 39
DSolve[{Derivative[1][x][t] == Cos[t]*x[t], Derivative[1][y][t] == x[t]/E^sin[t]},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to c_1 e^{\sin (t)},y(t)\to c_1 \int _1^te^{\sin (K[1])-\sin (K[1])}dK[1]+c_2\right \}\right \}\] ✓ Maple : cpu = 0.171 (sec), leaf count = 18
dsolve({diff(x(t),t) = x(t)*cos(t), diff(y(t),t) = x(t)*exp(-sin(t))})
\[\{x \left (t \right ) = c_{2} {\mathrm e}^{\sin \left (t \right )}, y \left (t \right ) = t c_{2}+c_{1}\}\]