  We approximate the spectra of a class of $2n$-order differential operators
using isogeometric analysis in mixed formulations. This class includes a wide
range of differential operators such as those arising in elliptic, biharmonic,
Cahn-Hilliard, Swift-Hohenberg, and phase-field crystal equations. The spectra
of the differential operators are approximated by solving differential
eigenvalue problems in mixed formulations, which require auxiliary parameters.
The mixed isogeometric formulation when applying classical quadrature rules
leads to an eigenvalue error convergence of order $2p$ where $p$ is the order
of the underlying B-spline space. We improve this order to be $2p+2$ by
applying optimally-blended quadrature rules developed in \cite{20,52} and this
order is an optimum in the view of dispersion error. We also compare these
results with the mixed finite elements and show numerically that mixed
isogeometric analysis leads to significantly better spectral approximations.
