\[ \boxed { \left \{ t{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +2\,x \left ( t \right ) =t,t{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) - \left ( t+2 \right ) x \left ( t \right ) -ty \left ( t \right ) =-t \right \} } \]
Mathematica: cpu = 0.012502 (sec), leaf count = 39 \[ \left \{\left \{x(t)\to \frac {c_1}{t^2}+\frac {t}{3},y(t)\to -\frac {c_1}{t^2}+c_2 e^t-\frac {t}{3}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 39 \[ \left \{ \left \{ x \left ( t \right ) ={\frac {t}{3}}+{\frac {{\it \_C2 }}{{t}^{2}}},y \left ( t \right ) ={\frac {3\,{\it \_C1}\,{{\rm e}^{t}}{ t}^{2}-{t}^{3}-3\,{\it \_C2}}{3\,{t}^{2}}} \right \} \right \} \]