\[ \left \{a \left (x'(t)-y'(t)\right )+\text {b1} x(t)+x''(t)=\text {c1} e^{i \omega t},a \left (y'(t)-x'(t)\right )+\text {b2} y(t)+y''(t)=\text {c2} e^{i \omega t}\right \} \] ✓ Mathematica : cpu = 2128.89 (sec), leaf count = 3402
\[\left \{\left \{x(t)\to -a \text {b2} c_3 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]-a \text {b2} \text {Integrate}\left [a \text {c1} e^{i \omega K[3]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[3] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c2} e^{i \omega K[3]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[3] \text {$\#$1}} \text {$\#$1}^2+a e^{-K[3] \text {$\#$1}} \text {$\#$1}+\text {b1} e^{-K[3] \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[3],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+a c_4 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+a \text {Integrate}\left [a \text {c1} e^{i \omega K[4]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[4] \text {$\#$1}} \text {$\#$1}^2}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c2} e^{i \omega K[4]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[4] \text {$\#$1}} \text {$\#$1}^3+a e^{-K[4] \text {$\#$1}} \text {$\#$1}^2+\text {b1} e^{-K[4] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[4],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+c_2 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^2+a e^{t \text {$\#$1}} \text {$\#$1}+\text {b2} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {Integrate}\left [a \text {c2} e^{i \omega K[2]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[2] \text {$\#$1}} \text {$\#$1}^2}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c1} e^{i \omega K[2]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[2] \text {$\#$1}} \text {$\#$1}^3+a e^{-K[2] \text {$\#$1}} \text {$\#$1}^2+\text {b2} e^{-K[2] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[2],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^2+a e^{t \text {$\#$1}} \text {$\#$1}+\text {b2} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+c_1 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^3+2 a e^{t \text {$\#$1}} \text {$\#$1}^2+\text {b2} e^{t \text {$\#$1}} \text {$\#$1}+a \text {b2} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {Integrate}\left [a \text {c2} e^{i \omega K[1]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[1] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c1} e^{i \omega K[1]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[1] \text {$\#$1}} \text {$\#$1}^2+a e^{-K[1] \text {$\#$1}} \text {$\#$1}+\text {b2} e^{-K[1] \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[1],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^3+2 a e^{t \text {$\#$1}} \text {$\#$1}^2+\text {b2} e^{t \text {$\#$1}} \text {$\#$1}+a \text {b2} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],y(t)\to -a \text {b1} c_1 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]-a \text {b1} \text {Integrate}\left [a \text {c2} e^{i \omega K[1]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[1] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c1} e^{i \omega K[1]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[1] \text {$\#$1}} \text {$\#$1}^2+a e^{-K[1] \text {$\#$1}} \text {$\#$1}+\text {b2} e^{-K[1] \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[1],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+a c_2 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+a \text {Integrate}\left [a \text {c2} e^{i \omega K[2]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[2] \text {$\#$1}} \text {$\#$1}^2}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c1} e^{i \omega K[2]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[2] \text {$\#$1}} \text {$\#$1}^3+a e^{-K[2] \text {$\#$1}} \text {$\#$1}^2+\text {b2} e^{-K[2] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[2],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+c_4 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^2+a e^{t \text {$\#$1}} \text {$\#$1}+\text {b1} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {Integrate}\left [a \text {c1} e^{i \omega K[4]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[4] \text {$\#$1}} \text {$\#$1}^2}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c2} e^{i \omega K[4]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[4] \text {$\#$1}} \text {$\#$1}^3+a e^{-K[4] \text {$\#$1}} \text {$\#$1}^2+\text {b1} e^{-K[4] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[4],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^2+a e^{t \text {$\#$1}} \text {$\#$1}+\text {b1} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+c_3 \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^3+2 a e^{t \text {$\#$1}} \text {$\#$1}^2+\text {b1} e^{t \text {$\#$1}} \text {$\#$1}+a \text {b1} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {Integrate}\left [a \text {c1} e^{i \omega K[3]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[3] \text {$\#$1}} \text {$\#$1}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]+\text {c2} e^{i \omega K[3]} \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{-K[3] \text {$\#$1}} \text {$\#$1}^2+a e^{-K[3] \text {$\#$1}} \text {$\#$1}+\text {b1} e^{-K[3] \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ],\{K[3],1,t\},\text {Assumptions}\to \text {True}\right ] \text {RootSum}\left [\text {$\#$1}^4+2 a \text {$\#$1}^3+\text {b1} \text {$\#$1}^2+\text {b2} \text {$\#$1}^2+a \text {b1} \text {$\#$1}+a \text {b2} \text {$\#$1}+\text {b1} \text {b2}\& ,\frac {e^{t \text {$\#$1}} \text {$\#$1}^3+2 a e^{t \text {$\#$1}} \text {$\#$1}^2+\text {b1} e^{t \text {$\#$1}} \text {$\#$1}+a \text {b1} e^{t \text {$\#$1}}}{4 \text {$\#$1}^3+6 a \text {$\#$1}^2+2 \text {b1} \text {$\#$1}+2 \text {b2} \text {$\#$1}+a \text {b1}+a \text {b2}}\& \right ]\right \}\right \}\]
✓ Maple : cpu = 1.086 (sec), leaf count = 2511
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {i{{\rm e}^{i\omega \,t}}a{\it c1}\,\omega +i{{\rm e}^{i\omega \,t}}a{\it c2}\,\omega -{\it c1}\,{\omega }^{2}{{\rm e}^{i\omega \,t}}+{\it b2}\,{\it c1}\,{{\rm e}^{i\omega \,t}}}{-2\,ia{\omega }^{3}+ia{\it b1}\,\omega +ia{\it b2}\,\omega +{\omega }^{4}-{\it b1}\,{\omega }^{2}-{\it b2}\,{\omega }^{2}+{\it b1}\,{\it b2}}}+{\it \_C1}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) t}}+{\it \_C2}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) t}}+{\it \_C3}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) t}}+{\it \_C4}\,{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) t}},y \left ( t \right ) = \left ( {\frac { \left ( -{\it \_C4}\,{\omega }^{4}+2\,i{\it \_C4}\,a{\omega }^{3}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C4}\,\omega -{\it \_C4}\,{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -2\,{\it \_C4}\,a{\omega }^{4}+4\,i{\it \_C4}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,{\it b2}\,a \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C4}\,\omega -2\,{\it \_C4}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -{\it \_C4}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C4}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C4}\,\omega -{\it \_C4}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac {-{\it \_C4}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C4}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C4}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C4}\,\omega -{\it \_C4}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=4 \right ) t}}+ \left ( {\frac { \left ( -{\it \_C3}\,{\omega }^{4}+2\,i{\it \_C3}\,a{\omega }^{3}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -2\,{\it \_C3}\,a{\omega }^{4}+4\,i{\it \_C3}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,{\it b2}\,a \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C3}\,\omega -2\,{\it \_C3}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -{\it \_C3}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C3}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac {-{\it \_C3}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C3}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C3}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C3}\,\omega -{\it \_C3}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=3 \right ) t}}+ \left ( {\frac { \left ( -{\it \_C2}\,{\omega }^{4}+2\,i{\it \_C2}\,a{\omega }^{3}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C2}\,\omega -{\it \_C2}\,{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -2\,{\it \_C2}\,a{\omega }^{4}+4\,i{\it \_C2}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,{\it b2}\,a \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C2}\,\omega -2\,{\it \_C2}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -{\it \_C2}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C2}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C2}\,\omega -{\it \_C2}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac {-{\it \_C2}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C2}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C2}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C2}\,\omega -{\it \_C2}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=2 \right ) t}}+ \left ( {\frac { \left ( -{\it \_C1}\,{\omega }^{4}+2\,i{\it \_C1}\,a{\omega }^{3}+ \left ( {\it b1}+{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -ia{\it b1}-ia{\it b2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \right ) ^{3}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -2\,{\it \_C1}\,a{\omega }^{4}+4\,i{\it \_C1}\,{a}^{2}{\omega }^{3}+ \left ( 2\,a{\it b1}+2\,{\it b2}\,a \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -2\,i{a}^{2}{\it b1}-2\,i{a}^{2}{\it b2} \right ) {\it \_C1}\,\omega -2\,{\it \_C1}\,a{\it b1}\,{\it b2} \right ) \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) \right ) ^{2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac { \left ( -{\it \_C1}\,{\it b1}\,{\omega }^{4}+2\,i{\it \_C1}\,a{\it b1}\,{\omega }^{3}+ \left ( {{\it b1}}^{2}+{\it b1}\,{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -ia{{\it b1}}^{2}-ia{\it b1}\,{\it b2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,{{\it b1}}^{2}{\it b2} \right ) {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) }{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}}+{\frac {-{\it \_C1}\,a{\it b1}\,{\omega }^{4}+2\,i{\it \_C1}\,{a}^{2}{\it b1}\,{\omega }^{3}+ \left ( a{{\it b1}}^{2}+a{\it b1}\,{\it b2} \right ) {\it \_C1}\,{\omega }^{2}+ \left ( -i{a}^{2}{{\it b1}}^{2}-i{a}^{2}{\it b1}\,{\it b2} \right ) {\it \_C1}\,\omega -{\it \_C1}\,a{{\it b1}}^{2}{\it b2}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}} \right ) {{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b1}\,{\it b2},{\it index}=1 \right ) t}}+{\frac { \left ( -a{\it b2}\,{\it c2}\,{\omega }^{2}+ \left ( i{a}^{2}{\it b2}\,{\it c1}+i{a}^{2}{\it b2}\,{\it c2} \right ) \omega +a{\it b1}\,{\it b2}\,{\it c2} \right ) {{\rm e}^{i\omega \,t}}}{ \left ( {\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ \left ( ia{\it b1}+ia{\it b2} \right ) \omega +{\it b1}\,{\it b2} \right ) {\it b2}\,a}} \right \} \right \} \]