\[ \left \{a \left (x'(t)-y'(t)\right )+\text {b1} x(t)+x''(t)=\text {c1} e^{i \omega t},a \left (y'(t)-x'(t)\right )+\text {b2} y(t)+y''(t)=\text {c2} e^{i \omega t}\right \} \] ✓ Mathematica : cpu = 0.428017 (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 = 0.786 (sec), leaf count = 1056
\[\left \{x \relax (t ) = \frac {\left (-\mathit {c1} \,\omega ^{2}+i \left (\mathit {c1} +\mathit {c2} \right ) a \omega +\mathit {b2} \mathit {c1} \right ) {\mathrm e}^{i \omega t}}{\omega ^{4}-2 i a \,\omega ^{3}+\left (-\mathit {b1} -\mathit {b2} \right ) \omega ^{2}+i a \left (\mathit {b1} +\mathit {b2} \right ) \omega +\mathit {b1} \mathit {b2}}+c_{1} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =1\right ) t}+c_{2} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =2\right ) t}+c_{3} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =3\right ) t}+c_{4} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =4\right ) t}, y \relax (t ) = \frac {-4 \left (-\frac {\omega ^{4}}{2}+i a \,\omega ^{3}+\left (\frac {\mathit {b1}}{2}+\frac {\mathit {b2}}{2}\right ) \omega ^{2}-\frac {i a \left (\mathit {b1} +\mathit {b2} \right ) \omega }{2}-\frac {\mathit {b1} \mathit {b2}}{2}\right ) \left (\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =1\right )^{2} a +\frac {\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =1\right )^{3}}{2}+\frac {\mathit {b1} a}{2}+\frac {\mathit {b1} \RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =1\right )}{2}\right ) c_{1} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =1\right ) t}-4 \left (\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =2\right )^{2} a +\frac {\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =2\right )^{3}}{2}+\frac {\mathit {b1} a}{2}+\frac {\mathit {b1} \RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =2\right )}{2}\right ) \left (-\frac {\omega ^{4}}{2}+i a \,\omega ^{3}+\left (\frac {\mathit {b1}}{2}+\frac {\mathit {b2}}{2}\right ) \omega ^{2}-\frac {i a \left (\mathit {b1} +\mathit {b2} \right ) \omega }{2}-\frac {\mathit {b1} \mathit {b2}}{2}\right ) c_{2} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =2\right ) t}-4 c_{3} \left (\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =3\right )^{2} a +\frac {\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =3\right )^{3}}{2}+\frac {\mathit {b1} a}{2}+\frac {\mathit {b1} \RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =3\right )}{2}\right ) \left (-\frac {\omega ^{4}}{2}+i a \,\omega ^{3}+\left (\frac {\mathit {b1}}{2}+\frac {\mathit {b2}}{2}\right ) \omega ^{2}-\frac {i a \left (\mathit {b1} +\mathit {b2} \right ) \omega }{2}-\frac {\mathit {b1} \mathit {b2}}{2}\right ) {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =3\right ) t}-4 \left (\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =4\right )^{2} a +\frac {\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =4\right )^{3}}{2}+\frac {\mathit {b1} a}{2}+\frac {\mathit {b1} \RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =4\right )}{2}\right ) c_{4} \left (-\frac {\omega ^{4}}{2}+i a \,\omega ^{3}+\left (\frac {\mathit {b1}}{2}+\frac {\mathit {b2}}{2}\right ) \omega ^{2}-\frac {i a \left (\mathit {b1} +\mathit {b2} \right ) \omega }{2}-\frac {\mathit {b1} \mathit {b2}}{2}\right ) {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (\mathit {b1} +\mathit {b2} \right ) \textit {\_Z}^{2}+\left (\mathit {b1} a +\mathit {b2} a \right ) \textit {\_Z} +\mathit {b1} \mathit {b2} , \mathit {index} =4\right ) t}-{\mathrm e}^{i \omega t} \mathit {b2} \left (-\omega ^{2} \mathit {c2} +i \left (\mathit {c1} +\mathit {c2} \right ) a \omega +\mathit {c2} \mathit {b1} \right ) a}{2 \mathit {b2} \left (-\frac {\omega ^{4}}{2}+i a \,\omega ^{3}+\left (\frac {\mathit {b1}}{2}+\frac {\mathit {b2}}{2}\right ) \omega ^{2}-\frac {i a \left (\mathit {b1} +\mathit {b2} \right ) \omega }{2}-\frac {\mathit {b1} \mathit {b2}}{2}\right ) a}\right \}\]