\[ \left \{x'(t)+2 y(t)=3 t,y'(t)-2 x(t)=4\right \} \] ✓ Mathematica : cpu = 0.0369737 (sec), leaf count = 132
DSolve[{2*y[t] + Derivative[1][x][t] == 3*t, -2*x[t] + Derivative[1][y][t] == 4},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to \cos (2 t) \left (\frac {3}{2} t \sin (2 t)-\frac {5}{4} \cos (2 t)\right )-\sin (2 t) \left (\frac {5}{4} \sin (2 t)+\frac {3}{2} t \cos (2 t)\right )+c_1 \cos (2 t)-c_2 \sin (2 t),y(t)\to \cos (2 t) \left (\frac {5}{4} \sin (2 t)+\frac {3}{2} t \cos (2 t)\right )+\sin (2 t) \left (\frac {3}{2} t \sin (2 t)-\frac {5}{4} \cos (2 t)\right )+c_2 \cos (2 t)+c_1 \sin (2 t)\right \}\right \}\] ✓ Maple : cpu = 0.046 (sec), leaf count = 39
dsolve({diff(x(t),t)+2*y(t) = 3*t, diff(y(t),t)-2*x(t) = 4})
\[\left \{x \left (t \right ) = \sin \left (2 t \right ) c_{2}+\cos \left (2 t \right ) c_{1}-\frac {5}{4}, y \left (t \right ) = -\cos \left (2 t \right ) c_{2}+\sin \left (2 t \right ) c_{1}+\frac {3 t}{2}\right \}\]