\[ \left \{-\text {A0} y'(t)+\text {a1} x''(t)+\text {b1} x'(t)+\text {c1} x(t)=\text {B0} e^{i \omega t},\text {A0} x'(t)+\text {a2} y''(t)+\text {b2} y'(t)+\text {c2} y(t)=0\right \} \] ✗ Mathematica : cpu = 300.018 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 1.276 (sec), leaf count = 1579
\[ \left \{ \left \{ x \left ( t \right ) ={\frac { \left ( {\it a2}\,{\it a1}\, \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) \right ) ^{3}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) \right ) ^{2}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it b1}\,{\it b2} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) +{\it c2}\,{\it b1} \right ) {\it \_C1}\, \left ( -{\it a1}\,{\it a2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b2}+i{\it a2}\,{\it b1} \right ) {\omega }^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) t}}+ \left ( {\it a2}\,{\it a1}\, \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) \right ) ^{3}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) \right ) ^{2}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it b1}\,{\it b2} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) +{\it c2}\,{\it b1} \right ) {\it \_C2}\, \left ( -{\it a1}\,{\it a2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b2}+i{\it a2}\,{\it b1} \right ) {\omega }^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) t}}+{\it \_C3}\, \left ( {\it a2}\,{\it a1}\, \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) \right ) ^{3}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) \right ) ^{2}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it b1}\,{\it b2} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) +{\it c2}\,{\it b1} \right ) \left ( -{\it a1}\,{\it a2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b2}+i{\it a2}\,{\it b1} \right ) {\omega }^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) t}}+{\it \_C4}\, \left ( -{\it a1}\,{\it a2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b2}+i{\it a2}\,{\it b1} \right ) {\omega }^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) \left ( {\it a2}\,{\it a1}\, \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) \right ) ^{3}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) \right ) ^{2}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it b1}\,{\it b2} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) +{\it c2}\,{\it b1} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) t}}-{\it c1}\,B \left ( i\omega \,{\it b2}-{\it a2}\,{\omega }^{2}+{\it c2} \right ) A{{\rm e}^{i\omega \,t}}}{{\it c1}\, \left ( -{\it a1}\,{\it a2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b2}+i{\it a2}\,{\it b1} \right ) {\omega }^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) A}},y \left ( t \right ) ={\frac {i{{\rm e}^{i\omega \,t}}\omega \,BA}{-{\it a1}\,{\it a2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b2}+i{\it a2}\,{\it b1} \right ) {\omega }^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2}}}+{\it \_C1}\,{{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) t}}+{\it \_C2}\,{{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) t}}+{\it \_C3}\,{{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) t}}+{\it \_C4}\,{{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it b1}\,{\it a2} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) t}} \right \} \right \} \]