\[ \left \{\left (t^2+1\right ) x'(t)=y(t)-t x(t),\left (t^2+1\right ) y'(t)=-x(t)-t y(t)\right \} \] ✓ Mathematica : cpu = 0.0094575 (sec), leaf count = 53
DSolve[{(1 + t^2)*Derivative[1][x][t] == -(t*x[t]) + y[t], (1 + t^2)*Derivative[1][y][t] == -x[t] - t*y[t]},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to \frac {c_1}{t^2+1}+\frac {c_2 t}{t^2+1},y(t)\to \frac {c_2}{t^2+1}-\frac {c_1 t}{t^2+1}\right \}\right \}\] ✓ Maple : cpu = 0.047 (sec), leaf count = 35
dsolve({(t^2+1)*diff(x(t),t) = -t*x(t)+y(t), (t^2+1)*diff(y(t),t) = -x(t)-t*y(t)})
\[\left \{x \left (t \right ) = \frac {t c_{1}+c_{2}}{t^{2}+1}, y \left (t \right ) = \frac {-t c_{2}+c_{1}}{t^{2}+1}\right \}\]