\[ \left \{-\text {A0} y'(t)+\text {a1} x''(t)+\text {b1} x'(t)+\text {c1} x(t)=\text {B0} e^{i \omega t},\text {A0} x'(t)+\text {a2} y''(t)+\text {b2} y'(t)+\text {c2} y(t)=0\right \} \] ✓ Mathematica : cpu = 845.802 (sec), leaf count = 5562
\[\left \{\left \{x(t)\to -\text {A0} \text {a1}^2 \text {c2} c_3 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a2}^2-\text {A0} \text {a1}^2 \text {c2} \text {Integrate}\left [-\text {A0} \text {a1} \text {a2} \text {B0} e^{i \omega K[3]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{-\frac {K[3] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],\{K[3],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a2}^2+\text {A0} \text {a1} c_4 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a2}^2+\text {A0} \text {a1} \text {Integrate}\left [-\text {A0} \text {B0} e^{i \omega K[4]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{-\frac {K[4] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],\{K[4],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a2}^2+\text {a1} c_2 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {\text {a2} \text {c2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {a1}^2+\text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1} \text {a1}+e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a2}+\text {a1} \text {Integrate}\left [\frac {\text {B0} e^{i \omega K[2]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{-\frac {K[2] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^3+\text {a1} \text {b2} e^{-\frac {K[2] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} e^{-\frac {K[2] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ]}{\text {a1}},\{K[2],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {\text {a2} \text {c2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {a1}^2+\text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1} \text {a1}+e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a2}+c_1 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^3+\text {a2} \text {b1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {a1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {A0}^2 \text {a1} \text {a2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1} \text {a2} \text {b1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1}^2 \text {a2} \text {c2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ]+\text {Integrate}\left [\text {a2} \text {B0} e^{i \omega K[1]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {\text {a2} \text {c2} e^{-\frac {K[1] \text {$\#$1}}{\text {a1} \text {a2}}} \text {a1}^2+\text {b2} e^{-\frac {K[1] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1} \text {a1}+e^{-\frac {K[1] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],\{K[1],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^3+\text {a2} \text {b1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {a1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {A0}^2 \text {a1} \text {a2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1} \text {a2} \text {b1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1}^2 \text {a2} \text {c2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],y(t)\to \text {A0} \text {a2}^2 \text {c1} c_1 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a1}^2+\text {A0} \text {a2}^2 \text {c1} \text {Integrate}\left [\text {a2} \text {B0} e^{i \omega K[1]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {\text {a2} \text {c2} e^{-\frac {K[1] \text {$\#$1}}{\text {a1} \text {a2}}} \text {a1}^2+\text {b2} e^{-\frac {K[1] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1} \text {a1}+e^{-\frac {K[1] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],\{K[1],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a1}^2-\text {A0} \text {a2} c_2 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a1}^2-\text {A0} \text {a2} \text {Integrate}\left [\frac {\text {B0} e^{i \omega K[2]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{-\frac {K[2] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^3+\text {a1} \text {b2} e^{-\frac {K[2] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} e^{-\frac {K[2] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ]}{\text {a1}},\{K[2],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a1}^2+\text {a2} c_4 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {\text {a1} \text {c1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {a2}^2+\text {b1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1} \text {a2}+e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a1}+\text {a2} \text {Integrate}\left [-\text {A0} \text {B0} e^{i \omega K[4]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{-\frac {K[4] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],\{K[4],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {\text {a1} \text {c1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {a2}^2+\text {b1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1} \text {a2}+e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ] \text {a1}+c_3 \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^3+\text {a2} \text {b1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {a1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {A0}^2 \text {a1} \text {a2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1} \text {a2} \text {b1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1} \text {a2}^2 \text {c1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ]+\text {Integrate}\left [-\text {A0} \text {a1} \text {a2} \text {B0} e^{i \omega K[3]} \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{-\frac {K[3] \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ],\{K[3],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+\text {a2} \text {b1} \text {$\#$1}^3+\text {a1} \text {b2} \text {$\#$1}^3+\text {A0}^2 \text {a1} \text {a2} \text {$\#$1}^2+\text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}^2+\text {a1} \text {a2}^2 \text {c1} \text {$\#$1}^2+\text {a1}^2 \text {a2} \text {c2} \text {$\#$1}^2+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2} \text {$\#$1}+\text {a1}^3 \text {a2}^3 \text {c1} \text {c2}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^3+\text {a2} \text {b1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {a1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}^2+\text {A0}^2 \text {a1} \text {a2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1} \text {a2} \text {b1} \text {b2} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1} \text {a2}^2 \text {c1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1} e^{\frac {t \text {$\#$1}}{\text {a1} \text {a2}}}}{4 \text {$\#$1}^3+3 \text {a2} \text {b1} \text {$\#$1}^2+3 \text {a1} \text {b2} \text {$\#$1}^2+2 \text {A0}^2 \text {a1} \text {a2} \text {$\#$1}+2 \text {a1} \text {a2} \text {b1} \text {b2} \text {$\#$1}+2 \text {a1} \text {a2}^2 \text {c1} \text {$\#$1}+2 \text {a1}^2 \text {a2} \text {c2} \text {$\#$1}+\text {a1}^2 \text {a2}^2 \text {b2} \text {c1}+\text {a1}^2 \text {a2}^2 \text {b1} \text {c2}}\& \right ]\right \}\right \}\]
✓ Maple : cpu = 1.253 (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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 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{\it c1}}} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 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{\it c1}}} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 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{\it c1}}} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}}+{\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 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{\it c1}}} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 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{\it c1}}},y \left ( t \right ) ={\frac {iAB{{\rm e}^{i\omega \,t}}\omega }{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 c2}\,{\it b1}\,\omega -i{\it b2}\,{\it c1}\,\omega +{\it a1}\,{\it c2}\,{\omega }^{2}+{\it c1}\,{\it a2}\,{\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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \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 c1}\,{\it a2}+{\it b1}\,{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) t}} \right \} \right \} \]