This paper describes a method for solving ordinary differential eigenvalue problems of the form N( u) + λM( u) = 0, where N and M are linear differential operators and u(x) is a scaler variable. The boundary conditions are independent of λ. The problem is transformed into a matrix problem ∥ A + λB ∥ = 0. This is reduced to the standard eigenvalue problem ∥ Â + λI ∥ = 0 which is then solved by the Q - R algorithm. The computer program is organized so that it can solve a wide range of problems with minimal effort on the user's part. The method is applied to a hydrodynamic stability problem and compared to the shooting method.