\[ \left \{x'(t)=2 x(t),y'(t)=3 x(t)-2 y(t),z'(t)=2 y(t)+3 z(t)\right \} \] ✓ Mathematica : cpu = 0.007828 (sec), leaf count = 112
DSolve[{Derivative[1][x][t] == 2*x[t], Derivative[1][y][t] == 3*x[t] - 2*y[t], Derivative[1][z][t] == 2*y[t] + 3*z[t]},{x[t], y[t], z[t]},t]
\[\left \{\left \{x(t)\to c_1 e^{2 t},y(t)\to \frac {3}{4} c_1 e^{-2 t} \left (e^{4 t}-1\right )+c_2 e^{-2 t},z(t)\to \frac {3}{10} c_1 e^{-2 t} \left (2 e^t+3 e^{2 t}+4 e^{3 t}+1\right ) \left (e^t-1\right )^2+\frac {2}{5} c_2 e^{-2 t} \left (e^{5 t}-1\right )+c_3 e^{3 t}\right \}\right \}\] ✓ Maple : cpu = 0.098 (sec), leaf count = 52
dsolve({diff(x(t),t) = 2*x(t), diff(y(t),t) = 3*x(t)-2*y(t), diff(z(t),t) = 2*y(t)+3*z(t)})
\[\left \{x \left (t \right ) = c_{3} {\mathrm e}^{2 t}, y \left (t \right ) = \frac {3 c_{3} {\mathrm e}^{2 t}}{4}+c_{2} {\mathrm e}^{-2 t}, z \left (t \right ) = c_{1} {\mathrm e}^{3 t}-\frac {3 c_{3} {\mathrm e}^{2 t}}{2}-\frac {2 c_{2} {\mathrm e}^{-2 t}}{5}\right \}\]