Propagation of linear and nonlinear dust-acoustic waves (DAWs) in a magnetized three component dusty plasma consisting of negatively charged dust-particles, isothermal ions and electrons are investigated. The standard normal-mode analysis is used to study the stability condition of linear dust-acoustic waves. However, for nonlinear waves, a reductive perturbation theory is applied to obtain the Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous Zakharov- Kuznetsov-type (LIZKT) equation for the second-order perturbed potential. At the critical phase velocity, the coefficient of the nonlinear terms of the ZK and LIZKT equations vanishes. A new set of expansion physical parameters and stretched coordinates are then used to derive a modified Zakharov- Kuznetsov (MZK) equation for the first order perturbed potential and a linear inhomogeneous modified Zakharov-Kuznetsov-type (LIMZKT) equation for the second-order perturbed potential. Stationary solutions of the coupled equations, for both cases, are obtained using a renormalization method. The effects of the higher-order contributions, the external magnetic field, the phase velocity, and the directional cosine of the wave vector k along the x-axis on the nature of the solitary waves are also discussed.