\[ \left \{a \left (x'(t)-y'(t)\right )+\text {b1} x(t)+x''(t)=\text {c1} e^{i \omega t},a \left (y'(t)-x'(t)\right )+\text {b2} y(t)+y''(t)=\text {c2} e^{i \omega t}\right \} \] ✗ Mathematica : cpu = 300.005 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 1.103 (sec), leaf count = 1056
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {{{\rm e}^{i\omega \,t}} \left ( -{\it c1}\,{\omega }^{2}+i \left ( {\it c1}+{\it c2} \right ) a\omega +{\it c1}\,{\it b2} \right ) }{{\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+i \left ( {\it b1}+{\it b2} \right ) a\omega +{\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}+{\it b2}\,a \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}+{\it b2}\,a \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}+{\it b2}\,a \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) t}},y \left ( t \right ) ={\frac {1}{2\,{\it b2}\,a} \left ( -4\,{\it \_C1}\, \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b1}\,{\it b2} \right ) \left ( \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \right ) ^{2}a+1/2\, \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) t}}-4\,{\it \_C2}\, \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b1}\,{\it b2} \right ) \left ( \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \right ) ^{2}a+1/2\, \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) t}}-4\, \left ( \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) ^{2}a+1/2\, \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) {\it \_C3}\, \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b1}\,{\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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) t}}-4\, \left ( \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) ^{2}a+1/2\, \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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) {\it \_C4}\, \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b1}\,{\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}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) t}}-{\it b2}\,{{\rm e}^{i\omega \,t}}a \left ( -{\omega }^{2}{\it c2}+i \left ( {\it c1}+{\it c2} \right ) a\omega +{\it c2}\,{\it b1} \right ) \right ) \left ( -{\frac {{\omega }^{4}}{2}}+ia{\omega }^{3}+ \left ( {\frac {{\it b1}}{2}}+{\frac {{\it b2}}{2}} \right ) {\omega }^{2}-{\frac {i}{2}}a \left ( {\it b1}+{\it b2} \right ) \omega -{\frac {{\it b1}\,{\it b2}}{2}} \right ) ^{-1}} \right \} \right \} \]