\[ \left \{x'(t)+3 x(t)+4 y(t)=0,2 x(t)+y'(t)+5 y(t)=0\right \} \] ✓ Mathematica : cpu = 0.0057566 (sec), leaf count = 84
DSolve[{3*x[t] + 4*y[t] + Derivative[1][x][t] == 0, 2*x[t] + 5*y[t] + Derivative[1][y][t] == 0},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to \frac {1}{3} c_1 e^{-7 t} \left (2 e^{6 t}+1\right )-\frac {2}{3} c_2 e^{-7 t} \left (e^{6 t}-1\right ),y(t)\to \frac {1}{3} c_2 e^{-7 t} \left (e^{6 t}+2\right )-\frac {1}{3} c_1 e^{-7 t} \left (e^{6 t}-1\right )\right \}\right \}\] ✓ Maple : cpu = 0.046 (sec), leaf count = 35
dsolve({diff(x(t),t)+3*x(t)+4*y(t) = 0, diff(y(t),t)+2*x(t)+5*y(t) = 0})
\[\left \{x \left (t \right ) = c_{1} {\mathrm e}^{-t}+c_{2} {\mathrm e}^{-7 t}, y \left (t \right ) = -\frac {c_{1} {\mathrm e}^{-t}}{2}+c_{2} {\mathrm e}^{-7 t}\right \}\]