\[ \left \{a \left (x'(t)-y'(t)\right )+\text {b1} x(t)+x''(t)=\text {c1} e^{i \omega t},a \left (y'(t)-x'(t)\right )+\text {b2} y(t)+y''(t)=\text {c2} e^{i \omega t}\right \} \] ✗ Mathematica : cpu = 300.002 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.872 (sec), leaf count = 2511
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {i{{\rm e}^{i\omega \,t}}a{\it c1}\,\omega +i{{\rm e}^{i\omega \,t}}a{\it c2}\,\omega -{\it c1}\,{{\rm e}^{i\omega \,t}}{\omega }^{2}+{\it c1}\,{\it b2}\,{{\rm e}^{i\omega \,t}}}{-2\,ia{\omega }^{3}+ia{\it b1}\,\omega +ia{\it b2}\,\omega +{\omega }^{4}-{\it b1}\,{\omega }^{2}-{\it b2}\,{\omega }^{2}+{\it b1}\,{\it b2}}}+{\it \_C1}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) t}}+{\it \_C2}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) t}}+{\it \_C3}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) t}}+{\it \_C4}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) t}},y \left ( t \right ) = \left ( {\frac { \left ( -{\omega }^{4}{\it \_C4}+2\,ia{\omega }^{3}{\it \_C4}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C4}\,\omega -{\it b1}\,{\it b2}\,{\it \_C4} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -2\,{\it \_C4}\,a{\omega }^{4}+4\,i{\it \_C4}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,a{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C4}\,\omega -2\,{\it \_C4}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -{\it \_C4}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C4}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C4}\,\omega -{\it \_C4}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac {-{\it \_C4}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C4}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C4}\,\omega -{\it \_C4}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) t}}+ \left ( {\frac { \left ( -{\omega }^{4}{\it \_C3}+2\,i{\omega }^{3}{\it \_C3}\,a+ \left ( {\it b1}+{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,{\it b2}\,{\it b1} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -2\,{\it \_C3}\,a{\omega }^{4}+4\,i{\it \_C3}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,a{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C3}\,\omega -2\,{\it \_C3}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -{\it \_C3}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C3}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac {-{\it \_C3}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C3}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) t}}+ \left ( {\frac { \left ( -{\omega }^{4}{\it \_C2}+2\,ia{\omega }^{3}{\it \_C2}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C2}\,\omega -{\it b2}\,{\it \_C2}\,{\it b1} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -2\,{\it \_C2}\,a{\omega }^{4}+4\,i{\it \_C2}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,a{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C2}\,\omega -2\,{\it \_C2}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -{\it \_C2}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C2}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C2}\,\omega -{\it \_C2}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac {-{\it \_C2}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C2}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C2}\,\omega -{\it \_C2}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) t}}+ \left ( {\frac { \left ( -{\omega }^{4}{\it \_C1}+2\,ia{\omega }^{3}{\it \_C1}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,{\it b2}\,{\it b1} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -2\,{\it \_C1}\,a{\omega }^{4}+4\,i{\it \_C1}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,a{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C1}\,\omega -2\,{\it \_C1}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac { \left ( -{\it \_C1}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C1}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}}+{\frac {-{\it \_C1}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C1}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+a{\it b2} \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) t}}+{\frac { \left ( -a{\it b2}\,{\it c2}\,{\omega }^{2}+ \left ( i{a}^{2}{\it b2}\,{\it c1}+i{a}^{2}{\it b2}\,{\it c2} \right ) \omega +a{\it b1}\,{\it b2}\,{\it c2} \right ) {{\rm e}^{i\omega \,t}}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) a{\it b2}}} \right \} \right \} \]