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]