\[ \left \{x'(t)=f(t) x(t)+g(t) y(t),y'(t)=f(t) y(t)-g(t) x(t)\right \} \] ✓ Mathematica : cpu = 0.0065051 (sec), leaf count = 115
\[\left \{\left \{x(t)\to c_1 \exp \left (\int _1^tf(K[2])dK[2]\right ) \cos \left (\int _1^tg(K[1])dK[1]\right )+c_2 \exp \left (\int _1^tf(K[2])dK[2]\right ) \sin \left (\int _1^tg(K[1])dK[1]\right ),y(t)\to c_2 \exp \left (\int _1^tf(K[2])dK[2]\right ) \cos \left (\int _1^tg(K[1])dK[1]\right )-c_1 \exp \left (\int _1^tf(K[2])dK[2]\right ) \sin \left (\int _1^tg(K[1])dK[1]\right )\right \}\right \}\] ✓ Maple : cpu = 0.741 (sec), leaf count = 57
\[ \left \{ \left \{ x \left ( t \right ) ={{\rm e}^{\int \!\tan \left ( {\it \_C1}-\int \!g \left ( t \right ) \,{\rm d}t \right ) g \left ( t \right ) +f \left ( t \right ) \,{\rm d}t}}{\it \_C2},y \left ( t \right ) ={{\rm e}^{\int \!\tan \left ( {\it \_C1}-\int \!g \left ( t \right ) \,{\rm d}t \right ) g \left ( t \right ) +f \left ( t \right ) \,{\rm d}t}}{\it \_C2}\,\tan \left ( {\it \_C1}-\int \!g \left ( t \right ) \,{\rm d}t \right ) \right \} \right \} \]