\[ \boxed { \left \{ t{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) +2\,{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +tx \left ( t \right ) =0,t{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -t{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) -2\,y \left ( t \right ) =0 \right \} } \]
Mathematica: cpu = 0.022503 (sec), leaf count = 47 \[ \text {DSolve}\left [\left \{t x'(t)-t y'(t)-2 y(t)=0,t x''(t)+2 x'(t)+t x(t)=0\right \},\{x(t),y(t)\},t\right ] \]
Maple: cpu = 0.078 (sec), leaf count = 47 \[ \left \{ \left \{ x \left ( t \right ) ={\frac {\sin \left ( t \right ) { \it \_C2}+{\it \_C3}\,\cos \left ( t \right ) }{t}},y \left ( t \right ) = {\frac {\sin \left ( t \right ) {\it \_C2}\,t+\cos \left ( t \right ) { \it \_C3}\,t-2\,{\it \_C3}\,\sin \left ( t \right ) +2\,\cos \left ( t \right ) {\it \_C2}+{\it \_C1}}{{t}^{2}}} \right \} \right \} \]