\[ \left \{\text {a11} x''(t)+\text {a12} y''(t)+\text {b11} x'(t)+\text {b12} y'(t)+\text {c11} x(t)+\text {c12} y(t)=0,\text {a21} x''(t)+\text {a22} y''(t)+\text {b21} x'(t)+\text {b22} y'(t)+\text {c21} x(t)+\text {c22} y(t)=0\right \} \] ✓ Mathematica : cpu = 0.20708 (sec), leaf count = 7517
DSolve[{c11*x[t] + c12*y[t] + b11*Derivative[1][x][t] + b12*Derivative[1][y][t] + a11*Derivative[2][x][t] + a12*Derivative[2][y][t] == 0, c21*x[t] + c22*y[t] + b21*Derivative[1][x][t] + b22*Derivative[1][y][t] + a21*Derivative[2][x][t] + a22*Derivative[2][y][t] == 0},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to c_4 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text {$\#$1}^3+\text {a12} \text {b21} \text {$\#$1}^3-\text {a11} \text {b22} \text {$\#$1}^3+\text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}^2-\text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}^2-\text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {c11} \text {$\#$1}^2-\text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {c12} \text {$\#$1}^2-\text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}^2+\text {a12}^2 \text {a21} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}^2+\text {a11}^2 \text {a22} \text {c22} \text {$\#$1}^2-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} \text {$\#$1}+\text {a12}^3 \text {a21}^3 \text {c12} \text {c21}-\text {a11}^3 \text {a22}^3 \text {c12} \text {c21}+3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c12} \text {c21}-3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c12} \text {c21}-\text {a12}^3 \text {a21}^3 \text {c11} \text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {\text {a21}^2 \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^3-\text {a21}^2 \text {a22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^2-2 \text {a11} \text {a21} \text {a22} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^2+\text {a21} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}^2+2 \text {a11} \text {a21} \text {a22}^2 \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}+\text {a11}^2 \text {a22}^2 \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}-\text {a21} \text {a22} \text {b12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}-\text {a11} \text {a22} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}-\text {a11}^2 \text {a22}^3 \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a11} \text {a22}^2 \text {b12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}}{-4 \text {$\#$1}^3+3 \text {a22} \text {b11} \text {$\#$1}^2-3 \text {a21} \text {b12} \text {$\#$1}^2-3 \text {a12} \text {b21} \text {$\#$1}^2+3 \text {a11} \text {b22} \text {$\#$1}^2-2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}+2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}+2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}+2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}-2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}+2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}-2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}-2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}+\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}-\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}-\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}-\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}-\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}+\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}+\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ]-c_3 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text {$\#$1}^3+\text {a12} \text {b21} \text {$\#$1}^3-\text {a11} \text {b22} \text {$\#$1}^3+\text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}^2-\text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}^2-\text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {c11} \text {$\#$1}^2-\text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {c12} \text {$\#$1}^2-\text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}^2+\text {a12}^2 \text {a21} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}^2+\text {a11}^2 \text {a22} \text {c22} \text {$\#$1}^2-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} \text {$\#$1}+\text {a12}^3 \text {a21}^3 \text {c12} \text {c21}-\text {a11}^3 \text {a22}^3 \text {c12} \text {c21}+3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c12} \text {c21}-3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c12} \text {c21}-\text {a12}^3 \text {a21}^3 \text {c11} \text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {\text {a21}^2 \text {b22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^2-\text {a21}^2 \text {b12} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^2-\text {a21} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}^2-2 \text {a11} \text {a21} \text {a22} \text {b22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}+2 \text {a11} \text {a21} \text {a22} \text {b12} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}+\text {a21} \text {a22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}+\text {a11} \text {a22} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}+\text {a11}^2 \text {a22}^2 \text {b22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a11}^2 \text {a22}^2 \text {b12} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a11} \text {a22}^2 \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}}{-4 \text {$\#$1}^3+3 \text {a22} \text {b11} \text {$\#$1}^2-3 \text {a21} \text {b12} \text {$\#$1}^2-3 \text {a12} \text {b21} \text {$\#$1}^2+3 \text {a11} \text {b22} \text {$\#$1}^2-2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}+2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}+2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}+2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}-2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}+2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}-2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}-2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}+\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}-\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}-\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}-\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}-\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}+\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}+\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ]-c_2 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text {$\#$1}^3+\text {a12} \text {b21} \text {$\#$1}^3-\text {a11} \text {b22} \text {$\#$1}^3+\text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}^2-\text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}^2-\text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {c11} \text {$\#$1}^2-\text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {c12} \text {$\#$1}^2-\text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}^2+\text {a12}^2 \text {a21} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}^2+\text {a11}^2 \text {a22} \text {c22} \text {$\#$1}^2-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} \text {$\#$1}+\text {a12}^3 \text {a21}^3 \text {c12} \text {c21}-\text {a11}^3 \text {a22}^3 \text {c12} \text {c21}+3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c12} \text {c21}-3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c12} \text {c21}-\text {a12}^3 \text {a21}^3 \text {c11} \text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {-\text {a22}^2 \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}^3+\text {a21} \text {a22}^2 \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}^2+2 \text {a12} \text {a21} \text {a22} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}^2+\text {a22} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}^2-2 \text {a12} \text {a21}^2 \text {a22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}-\text {a12}^2 \text {a21}^2 \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}-\text {a22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2 \text {a11}-\text {a21} \text {a22} \text {b12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}-\text {a12} \text {a21} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}+\text {a12}^2 \text {a21}^3 \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a12} \text {a21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {b12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}}{-4 \text {$\#$1}^3+3 \text {a22} \text {b11} \text {$\#$1}^2-3 \text {a21} \text {b12} \text {$\#$1}^2-3 \text {a12} \text {b21} \text {$\#$1}^2+3 \text {a11} \text {b22} \text {$\#$1}^2-2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}+2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}+2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}+2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}-2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}+2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}-2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}-2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}+\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}-\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}-\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}-\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}-\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}+\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}+\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ]+c_1 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text {$\#$1}^3+\text {a12} \text {b21} \text {$\#$1}^3-\text {a11} \text {b22} \text {$\#$1}^3+\text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}^2-\text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}^2-\text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {c11} \text {$\#$1}^2-\text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {c12} \text {$\#$1}^2-\text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}^2+\text {a12}^2 \text {a21} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}^2+\text {a11}^2 \text {a22} \text {c22} \text {$\#$1}^2-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} \text {$\#$1}+\text {a12}^3 \text {a21}^3 \text {c12} \text {c21}-\text {a11}^3 \text {a22}^3 \text {c12} \text {c21}+3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c12} \text {c21}-3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c12} \text {c21}-\text {a12}^3 \text {a21}^3 \text {c11} \text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^3-\text {a22} \text {b11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a21} \text {b12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a12} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2-\text {a11} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a12} \text {a21} \text {b12} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a11} \text {a22} \text {b12} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a12} \text {a21} \text {b11} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a11} \text {a22} \text {b11} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a12} \text {a21}^2 \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a11} \text {a21} \text {a22} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a11} \text {a12} \text {a21} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a11}^2 \text {a22} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}}{4 \text {$\#$1}^3-3 \text {a22} \text {b11} \text {$\#$1}^2+3 \text {a21} \text {b12} \text {$\#$1}^2+3 \text {a12} \text {b21} \text {$\#$1}^2-3 \text {a11} \text {b22} \text {$\#$1}^2+2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}-2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}-2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}+2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}+2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}-2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}+2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}-2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}+2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}+2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ],y(t)\to c_2 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text {$\#$1}^3+\text {a12} \text {b21} \text {$\#$1}^3-\text {a11} \text {b22} \text {$\#$1}^3+\text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}^2-\text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}^2-\text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {c11} \text {$\#$1}^2-\text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {c12} \text {$\#$1}^2-\text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}^2+\text {a12}^2 \text {a21} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}^2+\text {a11}^2 \text {a22} \text {c22} \text {$\#$1}^2-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21} \text {$\#$1}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22} \text {$\#$1}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} \text {$\#$1}+\text {a12}^3 \text {a21}^3 \text {c12} \text {c21}-\text {a11}^3 \text {a22}^3 \text {c12} \text {c21}+3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c12} \text {c21}-3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c12} \text {c21}-\text {a12}^3 \text {a21}^3 \text {c11} \text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {-\text {a22}^2 \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}^3+\text {a21} \text {a22}^2 \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}^2+2 \text {a12} \text {a21} \text {a22} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}^2+\text {a22} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}^2-2 \text {a12} \text {a21}^2 \text {a22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}-\text {a12}^2 \text {a21}^2 \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a11}-\text {a21} \text {a22} \text {b11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}-\text {a12} \text {a21} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}+\text {a12}^2 \text {a21}^3 \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a12} \text {a21}^2 \text {b11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}}{-4 \text {$\#$1}^3+3 \text {a22} \text {b11} \text {$\#$1}^2-3 \text {a21} \text {b12} \text {$\#$1}^2-3 \text {a12} \text {b21} \text {$\#$1}^2+3 \text {a11} \text {b22} \text {$\#$1}^2-2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}+2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}+2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}+2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}-2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}+2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}-2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}-2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}+\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}-\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}-\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}-\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}-\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}+\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}+\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ]+c_1 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text {$\#$1}^3+\text {a12} \text {b21} \text {$\#$1}^3-\text {a11} \text {b22} \text {$\#$1}^3+\text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}^2-\text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}^2-\text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {c11} \text {$\#$1}^2-\text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}^2+\text {a12} \text {a21}^2 \text {c12} \text {$\#$1}^2-\text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}^2+\text {a12}^2 \text {a21} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}^2-\text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}^2+\text {a11}^2 \text {a22} \text {c22} \text {$\#$1}^2-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} \text {$\#$1}-\text {a11}^2 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\text {a22}}} \text {a11}-\text {a21} \text {a22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}-\text {a12} \text {a21} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a11}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a12} \text {a21}^2 \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}}{-4 \text {$\#$1}^3+3 \text {a22} \text {b11} \text {$\#$1}^2-3 \text {a21} \text {b12} \text {$\#$1}^2-3 \text {a12} \text {b21} \text {$\#$1}^2+3 \text {a11} \text {b22} \text {$\#$1}^2-2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}+2 \text {a11} \text {a22} \text {b12} \text {b21} \text 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{a11}^2 \text {a22}^2 \text {b11} \text {c22} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22} \text {$\#$1}+\text {a12}^3 \text {a21}^3 \text {c12} \text {c21}-\text {a11}^3 \text {a22}^3 \text {c12} \text {c21}+3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c12} \text {c21}-3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c12} \text {c21}-\text {a12}^3 \text {a21}^3 \text {c11} \text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {\text {a21}^2 \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^3-\text {a21}^2 \text {a22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^2-2 \text {a11} \text {a21} \text {a22} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}^2+\text {a21} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}^2+2 \text {a11} \text {a21} \text {a22}^2 \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}+\text {a11}^2 \text {a22}^2 \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {a12}+\text {a21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2 \text {a12}-\text {a21} \text {a22} \text {b11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}-\text {a11} \text {a22} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1} \text {a12}-\text {a11}^2 \text {a22}^3 \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a11} \text {a22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a11} \text {a22}^2 \text {b11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}}{-4 \text {$\#$1}^3+3 \text {a22} \text {b11} \text {$\#$1}^2-3 \text {a21} \text {b12} \text {$\#$1}^2-3 \text {a12} \text {b21} \text {$\#$1}^2+3 \text {a11} \text {b22} \text {$\#$1}^2-2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}+2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}+2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}-2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}+2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}-2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}+2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}-2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}+2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}-2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}+\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}+\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}-\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}-\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}-\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}-\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}+\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}+\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ]+c_3 \text {RootSum}\left [\text {$\#$1}^4-\text {a22} \text {b11} \text {$\#$1}^3+\text {a21} \text {b12} \text 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\text {c22}+\text {a11}^3 \text {a22}^3 \text {c11} \text {c22}-3 \text {a11}^2 \text {a12} \text {a21} \text {a22}^2 \text {c11} \text {c22}+3 \text {a11} \text {a12}^2 \text {a21}^2 \text {a22} \text {c11} \text {c22}\& ,\frac {e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^3-\text {a22} \text {b11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a21} \text {b12} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a12} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2-\text {a11} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}^2+\text {a12} \text {a21} \text {b12} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a11} \text {a22} \text {b12} \text {b21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a12} \text {a21} \text {b11} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a11} \text {a22} \text {b11} \text {b22} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a11} \text {a22}^2 \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a12} \text {a21} \text {a22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}+\text {a12}^2 \text {a21} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a11} \text {a12} \text {a22} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21} e^{\frac {t \text {$\#$1}}{\text {a12} \text {a21}-\text {a11} \text {a22}}}}{4 \text {$\#$1}^3-3 \text {a22} \text {b11} \text {$\#$1}^2+3 \text {a21} \text {b12} \text {$\#$1}^2+3 \text {a12} \text {b21} \text {$\#$1}^2-3 \text {a11} \text {b22} \text {$\#$1}^2+2 \text {a12} \text {a21} \text {b12} \text {b21} \text {$\#$1}-2 \text {a11} \text {a22} \text {b12} \text {b21} \text {$\#$1}-2 \text {a12} \text {a21} \text {b11} \text {b22} \text {$\#$1}+2 \text {a11} \text {a22} \text {b11} \text {b22} \text {$\#$1}+2 \text {a11} \text {a22}^2 \text {c11} \text {$\#$1}-2 \text {a12} \text {a21} \text {a22} \text {c11} \text {$\#$1}+2 \text {a12} \text {a21}^2 \text {c12} \text {$\#$1}-2 \text {a11} \text {a21} \text {a22} \text {c12} \text {$\#$1}+2 \text {a12}^2 \text {a21} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a22} \text {c21} \text {$\#$1}-2 \text {a11} \text {a12} \text {a21} \text {c22} \text {$\#$1}+2 \text {a11}^2 \text {a22} \text {c22} \text {$\#$1}-\text {a12}^2 \text {a21}^2 \text {b22} \text {c11}-\text {a11}^2 \text {a22}^2 \text {b22} \text {c11}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b22} \text {c11}+\text {a12}^2 \text {a21}^2 \text {b21} \text {c12}+\text {a11}^2 \text {a22}^2 \text {b21} \text {c12}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b21} \text {c12}+\text {a12}^2 \text {a21}^2 \text {b12} \text {c21}+\text {a11}^2 \text {a22}^2 \text {b12} \text {c21}-2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b12} \text {c21}-\text {a12}^2 \text {a21}^2 \text {b11} \text {c22}-\text {a11}^2 \text {a22}^2 \text {b11} \text {c22}+2 \text {a11} \text {a12} \text {a21} \text {a22} \text {b11} \text {c22}}\& \right ]\right \}\right \}\] ✓ Maple : cpu = 0.19 (sec), leaf count = 1008
dsolve({a11*diff(diff(x(t),t),t)+b11*diff(x(t),t)+c11*x(t)+a12*diff(diff(y(t),t),t)+b12*diff(y(t),t)+c12*y(t) = 0, a21*diff(diff(x(t),t),t)+b21*diff(x(t),t)+c21*x(t)+a22*diff(diff(y(t),t),t)+b22*diff(y(t),t)+c22*y(t) = 0})
\[\left \{x \left (t \right ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}, y \left (t \right ) = \frac {\left (\left (-\mathit {a21} \mathit {c22} +\mathit {b21} \mathit {b22} \right ) \mathit {a12}^{2}+\left (\left (\mathit {a11} \mathit {c22} +\mathit {a21} \mathit {c12} -\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \mathit {a22} -\mathit {a11} \,\mathit {b22}^{2}+\mathit {a21} \mathit {b12} \mathit {b22} \right ) \mathit {a12} +\mathit {a22} \left (\left (-\mathit {a11} \mathit {c12} +\mathit {b12} \mathit {b11} \right ) \mathit {a22} +\mathit {a11} \mathit {b12} \mathit {b22} -\mathit {a21} \,\mathit {b12}^{2}\right )\right ) \left (\moverset {4}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right )^{2} {\mathrm e}^{\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )-\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \left (\mathit {b22} \mathit {a12} -\mathit {a22} \mathit {b12} \right ) \left (\moverset {4}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right )^{3} {\mathrm e}^{\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )+\left (\left (-\mathit {b21} \mathit {c22} +\mathit {b22} \mathit {c21} \right ) \mathit {a12}^{2}+\left (\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} +\mathit {b21} \mathit {c12} -\mathit {b22} \mathit {c11} \right ) \mathit {a22} -\mathit {b22}^{2} \mathit {b11} +\mathit {b21} \mathit {b12} \mathit {b22} \right ) \mathit {a12} +\mathit {a22} \left (\left (-\mathit {b11} \mathit {c12} +\mathit {b12} \mathit {c11} \right ) \mathit {a22} +\mathit {b22} \mathit {b11} \mathit {b12} -\mathit {b21} \,\mathit {b12}^{2}\right )\right ) \left (\moverset {4}{\munderset {\textit {\_a} =1}{\sum }}\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right ) {\mathrm e}^{\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right )-\left (\moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (\left (\mathit {a22} \mathit {a11} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b22} \mathit {b11} -\mathit {b21} \mathit {b12} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {b12} \mathit {c21} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c12} \mathit {c21} , \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}}\right ) \left (\mathit {a12}^{2} \mathit {c21} \mathit {c22} +\left (-\mathit {a22} \mathit {c11} \mathit {c22} -\mathit {a22} \mathit {c12} \mathit {c21} -\mathit {b12} \mathit {b22} \mathit {c21} +\mathit {b22}^{2} \mathit {c11} \right ) \mathit {a12} +\mathit {a22}^{2} \mathit {c11} \mathit {c12} +\left (\mathit {b12}^{2} \mathit {c21} -\mathit {b12} \mathit {b22} \mathit {c11} \right ) \mathit {a22} \right )}{\mathit {c22}^{2} \mathit {a12}^{2}+\left (-2 \mathit {a22} \mathit {c12} \mathit {c22} -\mathit {b12} \mathit {b22} \mathit {c22} +\mathit {c12} \,\mathit {b22}^{2}\right ) \mathit {a12} +\mathit {a22}^{2} \mathit {c12}^{2}+\left (\mathit {b12}^{2} \mathit {c22} -\mathit {b12} \mathit {c12} \mathit {b22} \right ) \mathit {a22}}\right \}\]