The similarity differential equation f'''+ f f'' + beta f' (f'- 1) - 0 with beta >0 is considered. This differential equation appears in the study of mixed convection boundary-layer flows over a vertical surface embedded in a porous medium. In order to prove the existence of solutions satisfying the boundary conditions f (0) = a >= 0, f' (0) = b >= 0 and f' (+ infinity) = 0 or 1, we use shooting and consider the initial value problem consisting of the differential equation and the initial conditions f (0) = a, f' (0) = b and f'' ( 0) = c. For 0 < beta1, we give only partial results and show some differences with the previous case.