In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow. The equation is:
with  the flow velocity of the steady base flow whose stability is to be studied and  is the cross-stream direction (i.e. perpendicular to the flow direction). Further  is the complex valued amplitude of the infinitesimal streamfunction perturbations applied to the base flow,  is the wavenumber of the perturbations and  is the phase speed with which the perturbations propagate in the flow direction. The prime denotes differentiation with respect to