This chapter applies the results of the general theory of homogeneous dynamics, Chap. 28 , to the special case, where \(m=1\) and the governing functions are linear. The linear system is of course well known, but our solution technique, based on calculus instead of linear algebra, is novel and helpful in obtaining relevant classification of solutions and the phase portraits. Rather than the traditional dichotomy, stable/unstable, we illustrate the use of the kinematic stability concepts for the ratio and coordinate solutions in global and generic versions. Bifurcation and structural stability are related to the regions in the parameter space, as are the kinematic stability properties. The solutions are obtained without coordinate transformations, and the main types of solutions for linear dynamics are classified directly with the parameters ( \(a,b,c,d\) ), without the calculation of the traditional eigenvalues. The parametric extension to affine dynamics supplements the linear dynamics.