\[ \boxed { \left \{ {t}^{2} \left ( 1-\sin \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =t \left ( 1-2\,\sin \left ( t \right ) \right ) x \left ( t \right ) +{t}^{2}y \left ( t \right ) ,{t}^{2} \left ( 1-\sin \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) = \left ( t\cos \left ( t \right ) -\sin \left ( t \right ) \right ) x \left ( t \right ) +t \left ( 1-t\cos \left ( t \right ) \right ) y \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.021503 (sec), leaf count = 79 \[ \text {DSolve}\left [\left \{t^2 (1-\sin (t)) x'(t)=t^2 y(t)+t x(t) (1-2 \sin (t)),t^2 (1-\sin (t)) y'(t)=x(t) (t \cos (t)-\sin (t))+t y(t) (1-t \cos (t))\right \},\{x(t),y(t)\},t\right ] \]
Maple: cpu = 0 (sec), leaf count = 0 \[ \text {hanged} \]