\[ \boxed { \left \{ t{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +2\,x \left ( t \right ) -2\,y \left ( t \right ) =t,t{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) +x \left ( t \right ) +5\,y \left ( t \right ) ={t}^{2} \right \} } \]
Mathematica: cpu = 0.057507 (sec), leaf count = 58 \[ \left \{\left \{x(t)\to \frac {c_1}{t^4}+\frac {c_2}{t^3}+\frac {1}{30} t (2 t+9),y(t)\to -\frac {c_1}{t^4}-\frac {c_2}{2 t^3}+\frac {1}{60} t (8 t-3)\right \}\right \} \]
Maple: cpu = 0.046 (sec), leaf count = 54 \[ \left \{ \left \{ x \left ( t \right ) ={\frac {2\,{t}^{6}+9\,{t}^{5}+30 \,t{\it \_C2}+30\,{\it \_C1}}{30\,{t}^{4}}},y \left ( t \right ) =-{ \frac {-8\,{t}^{6}+3\,{t}^{5}+30\,t{\it \_C2}+60\,{\it \_C1}}{60\,{t}^ {4}}} \right \} \right \} \]