\[ \left \{x'(t)=\text {a1} x(t)+\text {b1} y(t)+\text {c1},y'(t)=\text {a2} x(t)+\text {b2} y(t)+\text {c2}\right \} \] ✓ Mathematica : cpu = 1.30738 (sec), leaf count = 926
\[\left \{\left \{x(t)\to \frac {2 e^{-\frac {1}{2} \left (\text {a1}+\text {b2}+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}\right ) t} \left (\text {a1} e^{(\text {a1}+\text {b2}) t} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1 \text {b2}^2+2 \sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \text {c1} e^{\frac {1}{2} \left (\text {a1}+\text {b2}+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}\right ) t} \text {b2}-e^{(\text {a1}+\text {b2}) t} \left (\left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1 \text {a1}^2+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \left (1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1 \text {a1}+2 \text {b1} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_2 \text {a1}+\text {a2} \text {b1} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1\right ) \text {b2}+\text {b1} \left (\text {a2} e^{(\text {a1}+\text {b2}) t} \left (\text {a1} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \left (1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1+2 \text {b1} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_2\right )-2 \sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \text {c2} e^{\frac {1}{2} \left (\text {a1}+\text {b2}+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}\right ) t}\right )\right )}{(4 \text {a2} \text {b1}-4 \text {a1} \text {b2}) \sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}},y(t)\to \frac {e^{-\frac {1}{2} \left (\text {a1}+\text {b2}+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}\right ) t} \left (4 \text {b1} e^{(\text {a1}+\text {b2}) t} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) c_1 \text {a2}^2-4 \sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \text {c1} e^{\frac {1}{2} \left (\text {a1}+\text {b2}+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}\right ) t} \text {a2}+2 e^{(\text {a1}+\text {b2}) t} \left (\text {b1} \left (\text {b2} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right )+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \left (1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right )\right ) c_2-\text {a1} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right ) \left (2 \text {b2} c_1+\text {b1} c_2\right )\right ) \text {a2}+4 \text {a1} \sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \text {c2} e^{\frac {1}{2} \left (\text {a1}+\text {b2}+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}\right ) t}-2 \text {a1} \text {b2} e^{(\text {a1}+\text {b2}) t} \left (-e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t} \text {a1}+\text {a1}+\text {b2} \left (-1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right )+\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} \left (1+e^{\sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}} t}\right )\right ) c_2\right )}{(4 \text {a2} \text {b1}-4 \text {a1} \text {b2}) \sqrt {\text {a1}^2-2 \text {b2} \text {a1}+\text {b2}^2+4 \text {a2} \text {b1}}}\right \}\right \}\]
✓ Maple : cpu = 0.193 (sec), leaf count = 224
\[ \left \{ \left \{ x \left ( t \right ) ={{\rm e}^{{\frac {t}{2} \left ( {\it a1}+{\it b2}+\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}} \right ) }}}{\it \_C2}+{{\rm e}^{{\frac {t}{2} \left ( {\it a1}+{\it b2}-\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}} \right ) }}}{\it \_C1}+{\frac {{\it c2}\,{\it b1}-{\it c1}\,{\it b2}}{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}},y \left ( t \right ) ={\frac {1}{2\,{\it b1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( -{\it \_C1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+{\it a1}-{\it b2} \right ) {{\rm e}^{{\frac {t}{2} \left ( {\it a1}+{\it b2}-\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}} \right ) }}}+{\it \_C2}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1}+{\it b2} \right ) {{\rm e}^{{\frac {t}{2} \left ( {\it a1}+{\it b2}+\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}} \right ) }}}-2\,{\it b1}\, \left ( {\it a1}\,{\it c2}-{\it a2}\,{\it c1} \right ) \right ) } \right \} \right \} \]