\[ \left \{x'(t)=2 x(t),y'(t)=3 x(t)-2 y(t),z'(t)=2 y(t)+3 z(t)\right \} \] ✓ Mathematica : cpu = 0.0138776 (sec), leaf count = 112
\[\left \{\left \{x(t)\to c_1 e^{2 t},y(t)\to \frac {3}{4} c_1 e^{-2 t} \left (e^{4 t}-1\right )+c_2 e^{-2 t},z(t)\to \frac {3}{10} c_1 e^{-2 t} \left (2 e^t+3 e^{2 t}+4 e^{3 t}+1\right ) \left (e^t-1\right )^2+\frac {2}{5} c_2 e^{-2 t} \left (e^{5 t}-1\right )+c_3 e^{3 t}\right \}\right \}\] ✓ Maple : cpu = 0.091 (sec), leaf count = 52
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C3}\,{{\rm e}^{2\,t}},y \left ( t \right ) ={\frac {3\,{\it \_C3}\,{{\rm e}^{2\,t}}}{4}}+{{\rm e}^{-2\,t}}{\it \_C2},z \left ( t \right ) ={\it \_C1}\,{{\rm e}^{3\,t}}-{\frac {3\,{\it \_C3}\,{{\rm e}^{2\,t}}}{2}}-{\frac {2\,{{\rm e}^{-2\,t}}{\it \_C2}}{5}} \right \} \right \} \]