\[ \left \{-\text {A0} y'(t)+\text {a1} x''(t)+\text {b1} x'(t)+\text {c1} x(t)=\text {B0} e^{i \omega t},\text {A0} x'(t)+\text {a2} y''(t)+\text {b2} y'(t)+\text {c2} y(t)=0\right \} \] ✓ Mathematica : cpu = 0.438235 (sec), leaf count = 5546
\[\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} 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}^2 \text {c2} \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 ] \int _1^t-\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 ]dK[3] \text {a2}^2+\text {A0} \text {a1} \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 ] \int _1^t-\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 ]dK[4] \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 {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 ] \int _1^t\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}}dK[2] \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 {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 ] \int _1^t\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 ]dK[1],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} 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}^2 \text {c1} \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 ] \int _1^t\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 ]dK[1] \text {a1}^2-\text {A0} \text {a2} \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 ] \int _1^t\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}}dK[2] \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 {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 ] \int _1^t-\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 ]dK[4] \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 {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 ] \int _1^t-\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 ]dK[3]\right \}\right \}\] ✓ Maple : cpu = 0.84 (sec), leaf count = 1579
\[ \left \{ \left \{ x \left ( t \right ) ={\frac { \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 b2}\,{\it b1} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {\it \_C1}\, \left ( {\it a2}\,{\it a1}\, \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 b2}\,{\it b1} \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 b2}+{\it a2}\,{\it b1} \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 b2}\,{\it b1} \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 ( {A}^{2}+{\it a1}\,{\it c2}+{\it b2}\,{\it b1} \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 b2}\,{\it b1} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=1 \right ) +{\it c2}\,{\it b1} \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 b2}\,{\it b1} \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}}+ \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 b2}\,{\it b1} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) \left ( {\it a2}\,{\it a1}\, \left ( {\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b2}\,{\it b1} \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 b2}+{\it a2}\,{\it b1} \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 b2}\,{\it b1} \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 ( {A}^{2}+{\it a1}\,{\it c2}+{\it b2}\,{\it b1} \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 b2}\,{\it b1} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=2 \right ) +{\it c2}\,{\it b1} \right ) {\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 b2}\,{\it b1} \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 ( -{\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 b2}\,{\it b1} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {\it \_C3}\, \left ( {\it a2}\,{\it a1}\, \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 b2}\,{\it b1} \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 b2}+{\it a2}\,{\it b1} \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 b2}\,{\it b1} \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 ( {A}^{2}+{\it a1}\,{\it c2}+{\it b2}\,{\it b1} \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 b2}\,{\it b1} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=3 \right ) +{\it c2}\,{\it b1} \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 b2}\,{\it b1} \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 ( -{\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 b2}\,{\it b1} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {\it \_C4}\, \left ( {\it a2}\,{\it a1}\, \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 b2}\,{\it b1} \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 b2}+{\it a2}\,{\it b1} \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 b2}\,{\it b1} \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 ( {A}^{2}+{\it a1}\,{\it c2}+{\it b2}\,{\it b1} \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 b2}\,{\it b1} \right ) {{\it \_Z}}^{2}+ \left ( {\it c2}\,{\it b1}+{\it b2}\,{\it c1} \right ) {\it \_Z}+{\it c1}\,{\it c2},{\it index}=4 \right ) +{\it c2}\,{\it b1} \right ) {{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b2}\,{\it b1} \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}}-A \left ( i\omega \,{\it b2}-{\it a2}\,{\omega }^{2}+{\it c2} \right ) {{\rm e}^{i\omega \,t}}B{\it c1}}{A \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 b2}\,{\it b1} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2} \right ) {\it c1}}},y \left ( t \right ) ={\frac {iBA{{\rm e}^{i\omega \,t}}\omega }{-{\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 b2}\,{\it b1} \right ) {\omega }^{2}+ \left ( -i{\it b1}\,{\it c2}-i{\it b2}\,{\it c1} \right ) \omega -{\it c1}\,{\it c2}}}+{\it \_C1}\,{{\rm e}^{{\it RootOf} \left ( {\it a1}\,{\it a2}\,{{\it \_Z}}^{4}+ \left ( {\it a1}\,{\it b2}+{\it a2}\,{\it b1} \right ) {{\it \_Z}}^{3}+ \left ( {A}^{2}+{\it a1}\,{\it c2}+{\it a2}\,{\it c1}+{\it b2}\,{\it b1} \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 a2}\,{\it c1}+{\it b2}\,{\it b1} \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 a2}\,{\it c1}+{\it b2}\,{\it b1} \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 a2}\,{\it c1}+{\it b2}\,{\it b1} \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 \} \]