2.1893   ODE No. 1893

\[ \left \{-\text {A0} y'(t)+\text {a1} x''(t)+\text {b1} x'(t)+\text {c1} x(t)=\text {B0} e^{i \omega t},\text {A0} x'(t)+\text {a2} y''(t)+\text {b2} y'(t)+\text {c2} y(t)=0\right \} \] ✓ Mathematica : cpu = 0.228076 (sec), leaf count = 5546

DSolve[{c1*x[t] + b1*Derivative[1][x][t] - A0*Derivative[1][y][t] + a1*Derivative[2][x][t] == B0*E^(I*omega*t), c2*y[t] + A0*Derivative[1][x][t] + b2*Derivative[1][y][t] + a2*Derivative[2][y][t] == 0},{x[t], y[t]},t]
 

\[\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 = 0.675 (sec), leaf count = 1565

dsolve({a1*diff(diff(x(t),t),t)+b1*diff(x(t),t)+c1*x(t)-A*diff(y(t),t) = B*exp(I*omega*t), a2*diff(diff(y(t),t),t)+b2*diff(y(t),t)+c2*y(t)+A*diff(x(t),t) = 0})
 

\[\text {Expression too large to display}\]