  We discuss a semi-analytical solution of the transport equation for electrons
at a non-relativistic shock in the presence of synchrotron energy losses. We
calculate the spectrum of accelerated (test) particles at any point upstream
and downstream of the shock for an arbitrary diffusion coefficient and we
specialize the results to three cases: 1) diffusion constant in momentum
($D(p)=D_{0}$), 2) Bohm diffusion ($D(p)\propto p$), and 3) Kolmogorov
diffusion ($D(p)\propto p^{1/3}$). Of special importance is the determination
of the shape of the cutoff in the electron spectrum which depends on the
diffusion properties felt by particles in the shock region. The formalism can
be generalized to the case of a shock with an upstream precursor induced by the
dynamical reaction of accelerated particles.
