\[ \left \{t^2 (1-\sin (t)) x'(t)=t^2 y(t)+t x(t) (1-2 \sin (t)),t^2 (1-\sin (t)) y'(t)=x(t) (t \cos (t)-\sin (t))+t y(t) (1-t \cos (t))\right \} \] ✗ Mathematica : cpu = 0.0149678 (sec), leaf count = 0 , could not solve
DSolve[{t^2*(1 - Sin[t])*Derivative[1][x][t] == t*(1 - 2*Sin[t])*x[t] + t^2*y[t], t^2*(1 - Sin[t])*Derivative[1][y][t] == (t*Cos[t] - Sin[t])*x[t] + t*(1 - t*Cos[t])*y[t]}, {x[t], y[t]}, t]
✓ Maple : cpu = 0.074 (sec), leaf count = 23
\[ \left \{ \left \{ x \left ( t \right ) =t \left ( {\it \_C1}\,t+{\it \_C2} \right ) ,y \left ( t \right ) =\sin \left ( t \right ) {\it \_C2}+{\it \_C1}\,t \right \} \right \} \]