  This paper deals with the two-dimensional incompressible, laminar,
steady-state boundary layer equations.First, we determine a family of velocity
distributions outside the boundary layer such that these problems may have
similarity solutions.Then, We examine in detail new exact solutions, called
{\it Pseudo-similarity}, where the external velocity varies inversely-linear
with the distance in the $x$-direction along the surface ($U_e(x) = U_\infty
x^{-1}). $ The analysis shows that solutions exist only for a lateral suction.
Here it is assumed that the flow is induced by a continuous permeable surface
with the stretching velocity $ U_wx^{-1}.$ For specified conditions, we
establish the existence of an infinite number of solutions, including monotonic
solutions and solutions which oscillate an infinite number of times and tend to
a certain limit. The properties of solutions depend on the suction parameter.
Furthermore, making use of the fourth-order Runge-Kutta scheme together with
the shooting method, numerical solutions are obtained.
