\[ \left \{-\text {A0} y'(t)+\text {a1} x''(t)+\text {b1} x'(t)+\text {c1} x(t)=\text {B0} e^{i \omega t},\text {A0} x'(t)+\text {a2} y''(t)+\text {b2} y'(t)+\text {c2} y(t)=0\right \} \] ✗ Mathematica : cpu = 300.006 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 1.164 (sec), leaf count = 4516
\[ \left \{ \left \{ x \left ( t \right ) = \left ( {\frac { \left ( -{\it \_C4}\,{{\it a1}}^{2}{{\it a2}}^{2}{\omega }^{4}+ \left ( i{{\it a1}}^{2}{\it a2}\,{\it b2}+i{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C4}\,{\omega }^{3}+ \left ( {A}^{2}{\it a1}\,{\it a2}+{{\it a1}}^{2}{\it a2}\,{\it c2}+{\it a1}\,{{\it a2}}^{2}{\it c1}+{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}-i{\it a1}\,{\it a2}\,{\it b2}\,{\it c1} \right ) {\it \_C4}\,\omega -{\it \_C4}\,{\it a1}\,{\it a2}\,{\it c1}\,{\it c2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) \right ) ^{3}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{{\it a1}}^{2}{\it a2}\,{\it b2}-{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C4}\,{\omega }^{4}+ \left ( i{{\it a1}}^{2}{{\it b2}}^{2}+2\,i{\it a1}\,{\it a2}\,{\it b1}\,{\it b2}+i{{\it a2}}^{2}{{\it b1}}^{2} \right ) {\it \_C4}\,{\omega }^{3}+ \left ( \left ( {{\it a1}}^{2}{\it b2}+{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+ \left ( {\it a1}\,{\it a2}\,{\it b2}+{{\it a2}}^{2}{\it b1} \right ) {\it c1}+{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( {A}^{2}{\it a1}+{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( \left ( -i{\it a1}\,{\it b1}\,{\it b2}-i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}+ \left ( -i{\it a1}\,{{\it b2}}^{2}-i{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1} \right ) {\it \_C4}\,\omega + \left ( -{\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) {\it c1}\,{\it c2}\,{\it \_C4} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) \right ) ^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{A}^{2}{\it a1}\,{\it a2}-{{\it a1}}^{2}{\it a2}\,{\it c2}-{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C4}\,{\omega }^{4}+ \left ( \left ( i{{\it a1}}^{2}{\it b2}+i{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+i{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( i{A}^{2}{\it a1}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+i{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C4}\,{\omega }^{3}+ \left ( {{\it a1}}^{2}{{\it c2}}^{2}+ \left ( 2\,{A}^{2}{\it a1}+{\it a1}\,{\it a2}\,{\it c1}+2\,{\it a1}\,{\it b1}\,{\it b2} \right ) {\it c2}+ \left ( {A}^{2}{\it a2}+{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1}+{A}^{4}+2\,{A}^{2}{\it b1}\,{\it b2}+{{\it b1}}^{2}{{\it b2}}^{2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( -i{A}^{2}{\it b1}-i{\it a1}\,{\it b2}\,{\it c1}-i{{\it b1}}^{2}{\it b2} \right ) {\it c2}+ \left ( -i{A}^{2}{\it b2}-i{\it b1}\,{{\it b2}}^{2} \right ) {\it c1} \right ) {\it \_C4}\,\omega + \left ( -{\it a1}\,{\it c1}\,{{\it c2}}^{2}+ \left ( -{A}^{2}-{\it b1}\,{\it b2} \right ) {\it c1}\,{\it c2} \right ) {\it \_C4} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac {-{\it \_C4}\,{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b1}\,{\it b2}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}\,{\it \_C4}\,{\omega }^{3}+ \left ( {\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( {A}^{2}{\it b1}+{\it a2}\,{\it b1}\,{\it c1}+{{\it b1}}^{2}{\it b2} \right ) {\it c2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -i{{\it b1}}^{2}{{\it c2}}^{2}-i{\it b1}\,{\it b2}\,{\it c1}\,{\it c2} \right ) {\it \_C4}\,\omega -{\it \_C4}\,{\it b1}\,{\it c1}\,{{\it c2}}^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) t}}+ \left ( {\frac { \left ( -{\it \_C3}\,{{\it a1}}^{2}{{\it a2}}^{2}{\omega }^{4}+ \left ( i{{\it a1}}^{2}{\it a2}\,{\it b2}+i{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C3}\,{\omega }^{3}+ \left ( {A}^{2}{\it a1}\,{\it a2}+{{\it a1}}^{2}{\it a2}\,{\it c2}+{\it a1}\,{{\it a2}}^{2}{\it c1}+{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}-i{\it a1}\,{\it a2}\,{\it b2}\,{\it c1} \right ) {\it \_C3}\,\omega -{\it \_C3}\,{\it a1}\,{\it a2}\,{\it c1}\,{\it c2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) \right ) ^{3}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{{\it a1}}^{2}{\it a2}\,{\it b2}-{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C3}\,{\omega }^{4}+ \left ( i{{\it a1}}^{2}{{\it b2}}^{2}+2\,i{\it a1}\,{\it a2}\,{\it b1}\,{\it b2}+i{{\it a2}}^{2}{{\it b1}}^{2} \right ) {\it \_C3}\,{\omega }^{3}+ \left ( \left ( {{\it a1}}^{2}{\it b2}+{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+ \left ( {\it a1}\,{\it a2}\,{\it b2}+{{\it a2}}^{2}{\it b1} \right ) {\it c1}+{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( {A}^{2}{\it a1}+{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( \left ( -i{\it a1}\,{\it b1}\,{\it b2}-i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}+ \left ( -i{\it a1}\,{{\it b2}}^{2}-i{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1} \right ) {\it \_C3}\,\omega + \left ( -{\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) {\it c1}\,{\it c2}\,{\it \_C3} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) \right ) ^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{A}^{2}{\it a1}\,{\it a2}-{{\it a1}}^{2}{\it a2}\,{\it c2}-{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C3}\,{\omega }^{4}+ \left ( \left ( i{{\it a1}}^{2}{\it b2}+i{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+i{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( i{A}^{2}{\it a1}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+i{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C3}\,{\omega }^{3}+ \left ( {{\it a1}}^{2}{{\it c2}}^{2}+ \left ( 2\,{A}^{2}{\it a1}+{\it a1}\,{\it a2}\,{\it c1}+2\,{\it a1}\,{\it b1}\,{\it b2} \right ) {\it c2}+ \left ( {A}^{2}{\it a2}+{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1}+{A}^{4}+2\,{A}^{2}{\it b1}\,{\it b2}+{{\it b1}}^{2}{{\it b2}}^{2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( -i{A}^{2}{\it b1}-i{\it a1}\,{\it b2}\,{\it c1}-i{{\it b1}}^{2}{\it b2} \right ) {\it c2}+ \left ( -i{A}^{2}{\it b2}-i{\it b1}\,{{\it b2}}^{2} \right ) {\it c1} \right ) {\it \_C3}\,\omega + \left ( -{\it a1}\,{\it c1}\,{{\it c2}}^{2}+ \left ( -{A}^{2}-{\it b1}\,{\it b2} \right ) {\it c1}\,{\it c2} \right ) {\it \_C3} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac {-{\it \_C3}\,{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b1}\,{\it b2}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}\,{\it \_C3}\,{\omega }^{3}+ \left ( {\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( {A}^{2}{\it b1}+{\it a2}\,{\it b1}\,{\it c1}+{{\it b1}}^{2}{\it b2} \right ) {\it c2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -i{{\it b1}}^{2}{{\it c2}}^{2}-i{\it b1}\,{\it b2}\,{\it c1}\,{\it c2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,{\it b1}\,{\it c1}\,{{\it c2}}^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) t}}+ \left ( {\frac { \left ( -{\it \_C2}\,{{\it a1}}^{2}{{\it a2}}^{2}{\omega }^{4}+ \left ( i{{\it a1}}^{2}{\it a2}\,{\it b2}+i{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C2}\,{\omega }^{3}+ \left ( {A}^{2}{\it a1}\,{\it a2}+{{\it a1}}^{2}{\it a2}\,{\it c2}+{\it a1}\,{{\it a2}}^{2}{\it c1}+{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}-i{\it a1}\,{\it a2}\,{\it b2}\,{\it c1} \right ) {\it \_C2}\,\omega -{\it \_C2}\,{\it a1}\,{\it a2}\,{\it c1}\,{\it c2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) \right ) ^{3}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{{\it a1}}^{2}{\it a2}\,{\it b2}-{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C2}\,{\omega }^{4}+ \left ( i{{\it a1}}^{2}{{\it b2}}^{2}+2\,i{\it a1}\,{\it a2}\,{\it b1}\,{\it b2}+i{{\it a2}}^{2}{{\it b1}}^{2} \right ) {\it \_C2}\,{\omega }^{3}+ \left ( \left ( {{\it a1}}^{2}{\it b2}+{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+ \left ( {\it a1}\,{\it a2}\,{\it b2}+{{\it a2}}^{2}{\it b1} \right ) {\it c1}+{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( {A}^{2}{\it a1}+{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( \left ( -i{\it a1}\,{\it b1}\,{\it b2}-i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}+ \left ( -i{\it a1}\,{{\it b2}}^{2}-i{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1} \right ) {\it \_C2}\,\omega + \left ( -{\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) {\it c1}\,{\it c2}\,{\it \_C2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) \right ) ^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{A}^{2}{\it a1}\,{\it a2}-{{\it a1}}^{2}{\it a2}\,{\it c2}-{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C2}\,{\omega }^{4}+ \left ( \left ( i{{\it a1}}^{2}{\it b2}+i{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+i{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( i{A}^{2}{\it a1}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+i{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C2}\,{\omega }^{3}+ \left ( {{\it a1}}^{2}{{\it c2}}^{2}+ \left ( 2\,{A}^{2}{\it a1}+{\it a1}\,{\it a2}\,{\it c1}+2\,{\it a1}\,{\it b1}\,{\it b2} \right ) {\it c2}+ \left ( {A}^{2}{\it a2}+{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1}+{A}^{4}+2\,{A}^{2}{\it b1}\,{\it b2}+{{\it b1}}^{2}{{\it b2}}^{2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( -i{A}^{2}{\it b1}-i{\it a1}\,{\it b2}\,{\it c1}-i{{\it b1}}^{2}{\it b2} \right ) {\it c2}+ \left ( -i{A}^{2}{\it b2}-i{\it b1}\,{{\it b2}}^{2} \right ) {\it c1} \right ) {\it \_C2}\,\omega + \left ( -{\it a1}\,{\it c1}\,{{\it c2}}^{2}+ \left ( -{A}^{2}-{\it b1}\,{\it b2} \right ) {\it c1}\,{\it c2} \right ) {\it \_C2} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac {-{\it \_C2}\,{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b1}\,{\it b2}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}\,{\it \_C2}\,{\omega }^{3}+ \left ( {\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( {A}^{2}{\it b1}+{\it a2}\,{\it b1}\,{\it c1}+{{\it b1}}^{2}{\it b2} \right ) {\it c2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -i{{\it b1}}^{2}{{\it c2}}^{2}-i{\it b1}\,{\it b2}\,{\it c1}\,{\it c2} \right ) {\it \_C2}\,\omega -{\it \_C2}\,{\it b1}\,{\it c1}\,{{\it c2}}^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) t}}+ \left ( {\frac { \left ( -{\it \_C1}\,{{\it a1}}^{2}{{\it a2}}^{2}{\omega }^{4}+ \left ( i{{\it a1}}^{2}{\it a2}\,{\it b2}+i{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C1}\,{\omega }^{3}+ \left ( {A}^{2}{\it a1}\,{\it a2}+{{\it a1}}^{2}{\it a2}\,{\it c2}+{\it a1}\,{{\it a2}}^{2}{\it c1}+{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}-i{\it a1}\,{\it a2}\,{\it b2}\,{\it c1} \right ) {\it \_C1}\,\omega -{\it \_C1}\,{\it a1}\,{\it a2}\,{\it c1}\,{\it c2} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) \right ) ^{3}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{{\it a1}}^{2}{\it a2}\,{\it b2}-{\it a1}\,{{\it a2}}^{2}{\it b1} \right ) {\it \_C1}\,{\omega }^{4}+ \left ( i{{\it a1}}^{2}{{\it b2}}^{2}+2\,i{\it a1}\,{\it a2}\,{\it b1}\,{\it b2}+i{{\it a2}}^{2}{{\it b1}}^{2} \right ) {\it \_C1}\,{\omega }^{3}+ \left ( \left ( {{\it a1}}^{2}{\it b2}+{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+ \left ( {\it a1}\,{\it a2}\,{\it b2}+{{\it a2}}^{2}{\it b1} \right ) {\it c1}+{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( {A}^{2}{\it a1}+{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( \left ( -i{\it a1}\,{\it b1}\,{\it b2}-i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}+ \left ( -i{\it a1}\,{{\it b2}}^{2}-i{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1} \right ) {\it \_C1}\,\omega + \left ( -{\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) {\it c1}\,{\it c2}\,{\it \_C1} \right ) \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) \right ) ^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac { \left ( \left ( -{A}^{2}{\it a1}\,{\it a2}-{{\it a1}}^{2}{\it a2}\,{\it c2}-{\it a1}\,{\it a2}\,{\it b1}\,{\it b2} \right ) {\it \_C1}\,{\omega }^{4}+ \left ( \left ( i{{\it a1}}^{2}{\it b2}+i{\it a1}\,{\it a2}\,{\it b1} \right ) {\it c2}+i{\it a1}\,{\it b1}\,{{\it b2}}^{2}+ \left ( i{A}^{2}{\it a1}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it b2}+i{A}^{2}{\it a2}\,{\it b1} \right ) {\it \_C1}\,{\omega }^{3}+ \left ( {{\it a1}}^{2}{{\it c2}}^{2}+ \left ( 2\,{A}^{2}{\it a1}+{\it a1}\,{\it a2}\,{\it c1}+2\,{\it a1}\,{\it b1}\,{\it b2} \right ) {\it c2}+ \left ( {A}^{2}{\it a2}+{\it a2}\,{\it b1}\,{\it b2} \right ) {\it c1}+{A}^{4}+2\,{A}^{2}{\it b1}\,{\it b2}+{{\it b1}}^{2}{{\it b2}}^{2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -i{\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( -i{A}^{2}{\it b1}-i{\it a1}\,{\it b2}\,{\it c1}-i{{\it b1}}^{2}{\it b2} \right ) {\it c2}+ \left ( -i{A}^{2}{\it b2}-i{\it b1}\,{{\it b2}}^{2} \right ) {\it c1} \right ) {\it \_C1}\,\omega + \left ( -{\it a1}\,{\it c1}\,{{\it c2}}^{2}+ \left ( -{A}^{2}-{\it b1}\,{\it b2} \right ) {\it c1}\,{\it c2} \right ) {\it \_C1} \right ) {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}}+{\frac {-{\it \_C1}\,{\it a1}\,{\it a2}\,{\it b1}\,{\it c2}\,{\omega }^{4}+ \left ( i{\it a1}\,{\it b1}\,{\it b2}+i{\it a2}\,{{\it b1}}^{2} \right ) {\it c2}\,{\it \_C1}\,{\omega }^{3}+ \left ( {\it a1}\,{\it b1}\,{{\it c2}}^{2}+ \left ( {A}^{2}{\it b1}+{\it a2}\,{\it b1}\,{\it c1}+{{\it b1}}^{2}{\it b2} \right ) {\it c2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -i{{\it b1}}^{2}{{\it c2}}^{2}-i{\it b1}\,{\it b2}\,{\it c1}\,{\it c2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,{\it b1}\,{\it c1}\,{{\it c2}}^{2}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) t}}+{\frac { \left ( -iAB{\it b2}\,{\it c1}\,\omega +AB{\it a2}\,{\it c1}\,{\omega }^{2}-AB{\it c1}\,{\it c2} \right ) {{\rm e}^{i\omega \,t}}}{ \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 a2}\,{\it c1}+{\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 ) {\it c1}\,A}},y \left ( t \right ) ={\frac {iB{{\rm e}^{i\omega \,t}}\omega \,A}{i{\it a1}\,{\it b2}\,{\omega }^{3}+i{\it a2}\,{\it b1}\,{\omega }^{3}-{\it a1}\,{\it a2}\,{\omega }^{4}+{A}^{2}{\omega }^{2}-i{\it b1}\,{\it c2}\,\omega -i{\it c1}\,{\it b2}\,\omega +{\it a1}\,{\it c2}\,{\omega }^{2}+{\it a2}\,{\it c1}\,{\omega }^{2}+{\it b1}\,{\it b2}\,{\omega }^{2}-{\it c1}\,{\it c2}}}+{\it \_C1}\,{{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\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 a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\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 a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\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 a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it b1}\,{\it c2}+{\it c1}\,{\it b2} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) t}} \right \} \right \} \]