Abstract The equations of motion of the Hamiltonian formulation of quadratic gravity are computed explicitly. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor (discarding the cosmological constant). The symbolic computational tool Cadabra is employed. The linearized version of the equations of motion is presented, performing the longitudinal‐transverse decomposition. The linear equations are compared with the covariant field equations, finding that, if general‐relativity terms are active, the linear Hamiltonian formulation is valid only if the perturbative spatial metric is traceless, a condition that can be freely imposed by recurring to an arbitrary function. The equations of motion are applied on homogeneous and isotropic configurations, finding explicit solutions.