2.1874   ODE No. 1874

\[ \left \{x'(t)=f(t) x(t)+g(t) y(t),y'(t)=f(t) y(t)-g(t) x(t)\right \} \] Mathematica : cpu = 0.0075882 (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 = 0.457 (sec), leaf count = 57


\[\{x \relax (t ) = {\mathrm e}^{\int \left (\tan \left (c_{1}-\left (\int g \relax (t )d t \right )\right ) g \relax (t )+f \relax (t )\right )d t} c_{2}, y \relax (t ) = {\mathrm e}^{\int \left (\tan \left (c_{1}-\left (\int g \relax (t )d t \right )\right ) g \relax (t )+f \relax (t )\right )d t} c_{2} \tan \left (c_{1}-\left (\int g \relax (t )d t \right )\right )\}\]