\[ \boxed { \left \{ t{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +y \left ( t \right ) =0,t{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) +x \left ( t \right ) =0 \right \} } \]
Mathematica: cpu = 0.005001 (sec), leaf count = 31 \[ \left \{\left \{x(t)\to c_1 t+\frac {c_2}{t},y(t)\to \frac {c_2}{t}-c_1 t\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 31 \[ \left \{ \left \{ x \left ( t \right ) ={\frac {{\it \_C2}\,{t}^{2}+{ \it \_C1}}{t}},y \left ( t \right ) ={\frac {-{\it \_C2}\,{t}^{2}+{\it \_C1}}{t}} \right \} \right \} \]