\[ \left \{x'(t)=f(t) x(t)+g(t) y(t),y'(t)=f(t) y(t)-g(t) x(t)\right \} \] ✓ Mathematica : cpu = 0.010728 (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 = 0.556 (sec), leaf count = 57
\[\{\{x \left (t \right ) = c_{2} {\mathrm e}^{\int \left (g \left (t \right ) \tan \left (c_{1}-\left (\int g \left (t \right )d t \right )\right )+f \left (t \right )\right )d t}, y \left (t \right ) = c_{2} {\mathrm e}^{\int \left (g \left (t \right ) \tan \left (c_{1}-\left (\int g \left (t \right )d t \right )\right )+f \left (t \right )\right )d t} \tan \left (c_{1}-\left (\int g \left (t \right )d t \right )\right )\}\}\]