Spontaneous emission is one of the most fundamental quantum phenomena in optics. Following the seminal work of Purcell and in agreement with the Fermi's Golden Rule, its rate can be controlled with the photonic density of states (PDOS). In recent years, this effect has been demonstrated in metamaterials with hyperbolic dispersion--highly anisotropic composite materials, which have a broad-band singularity of the density of photonic states. At this time, we show that hyperbolic metamaterials can control spontaneous emission spectra as well. Experimentally, DCM laser dye has been embedded into lamellar metal/dielectric metamaterial. The observed 18 nm blue shift of emission is explained by strong dispersion of the density of photonic states. On the other hand, practically no spectral shift has been observed in the excitation spectra of the same dye. This suggests that the effect of PDOS on spontaneous emission is very different from its effect on excitation and absorption.