\[ \left \{a \left (x'(t)-y'(t)\right )+\text {b1} x(t)+x''(t)=\text {c1} e^{i \omega t},a \left (y'(t)-x'(t)\right )+\text {b2} y(t)+y''(t)=\text {c2} e^{i \omega t}\right \} \] ✓ Mathematica : cpu = 0.428619 (sec), leaf count = 3386
\[\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} \int _1^t\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 ]\right )dK[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 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 ]+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 ]+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 {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 ] \int _1^t\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 ]\right )dK[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}^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 ] \int _1^t\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 ]\right )dK[2]+a \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 ] \int _1^t\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 ]\right )dK[4],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} \int _1^t\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 ]\right )dK[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 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 ]+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 ]+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 {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 ] \int _1^t\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 ]\right )dK[3]+a \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 ] \int _1^t\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 ]\right )dK[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 {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 ] \int _1^t\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 ]\right )dK[4]\right \}\right \}\] ✓ Maple : cpu = 0.635 (sec), leaf count = 1056
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {{{\rm e}^{i\omega \,t}} \left ( -{\it c1}\,{\omega }^{2}+ia \left ( {\it c1}+{\it c2} \right ) \omega +{\it b2}\,{\it c1} \right ) }{{\omega }^{4}-2\,ia{\omega }^{3}+ \left ( -{\it b1}-{\it b2} \right ) {\omega }^{2}+ia \left ( {\it b1}+{\it b2} \right ) \omega +{\it b2}\,{\it b1}}}+{\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 b2}\,{\it b1},{\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 b2}\,{\it b1},{\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 b2}\,{\it b1},{\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 b2}\,{\it b1},{\it index}=4 \right ) t}},y \left ( t \right ) ={\frac {1}{2\,{\it b2}\,a} \left ( -4\, \left ( \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=1 \right ) \right ) ^{2}a+1/2\, \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=1 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=1 \right ) \right ) {\it \_C1}\, \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b2}\,{\it b1} \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 b2}\,{\it b1},{\it index}=1 \right ) t}}-4\, \left ( \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=2 \right ) \right ) ^{2}a+1/2\, \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=2 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=2 \right ) \right ) \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b2}\,{\it b1} \right ) {\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 b2}\,{\it b1},{\it index}=2 \right ) t}}-4\,{\it \_C3}\, \left ( \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=3 \right ) \right ) ^{2}a+1/2\, \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=3 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=3 \right ) \right ) \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b2}\,{\it b1} \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 b2}\,{\it b1},{\it index}=3 \right ) t}}-4\, \left ( \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=4 \right ) \right ) ^{2}a+1/2\, \left ( {\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=4 \right ) \right ) ^{3}+1/2\,a{\it b1}+1/2\,{\it b1}\,{\it RootOf} \left ( {{\it \_Z}}^{4}+2\,a{{\it \_Z}}^{3}+ \left ( {\it b1}+{\it b2} \right ) {{\it \_Z}}^{2}+ \left ( a{\it b1}+{\it b2}\,a \right ) {\it \_Z}+{\it b2}\,{\it b1},{\it index}=4 \right ) \right ) {\it \_C4}\, \left ( -1/2\,{\omega }^{4}+ia{\omega }^{3}+ \left ( {\it b1}/2+{\it b2}/2 \right ) {\omega }^{2}-i/2a \left ( {\it b1}+{\it b2} \right ) \omega -1/2\,{\it b2}\,{\it b1} \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 b2}\,{\it b1},{\it index}=4 \right ) t}}-a{{\rm e}^{i\omega \,t}}{\it b2}\, \left ( -{\omega }^{2}{\it c2}+ia \left ( {\it c1}+{\it c2} \right ) \omega +{\it c2}\,{\it b1} \right ) \right ) \left ( -{\frac {{\omega }^{4}}{2}}+ia{\omega }^{3}+ \left ( {\frac {{\it b1}}{2}}+{\frac {{\it b2}}{2}} \right ) {\omega }^{2}-{\frac {i}{2}}a \left ( {\it b1}+{\it b2} \right ) \omega -{\frac {{\it b2}\,{\it b1}}{2}} \right ) ^{-1}} \right \} \right \} \]