The Crocco equation for zero pressure gradient and a constant viscosity density product is linearized and the results applied to boundary-layer problems where the given initial profile is much different from the Blasius profile. Four linearization assumptions are used, each of which leads to an eigenvalue problem having a discrete spectrum of eigenvalues. This allows the shear stress to be expressed as a series. Far downstream of the initial station the first term of this series dominates. Solutions valid in this region are obtained for each assumption and are compared to the exact similar solution. The best assumptions are applied to two examples where it is desired to find the skin friction behind a region having mass injection. Comparison to finite difference solutions shows the present solution to be satisfactory and superior to solutions obtained by perturbations from the Blasius solution. The accuracy of the solution is improved by making multiple linearization assumptions in the streamwise direction and application is made to the problem of free mixing in the vicinity of a flat wall.