  In this paper, position vectors of a time-like curve with respect to standard
frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations.
First, we prove that position vector of every time-like space curve in
Minkowski space E$^3_1$ satisfies a vector differential equation of fourth
order. The general solution of mentioned vector differential equation has not
yet been found. By special cases, we determine the parametric representation of
the general helices from the intrinsic equations (i.e. curvature and torsion
are functions of arc-length) of the time-like curve. Moreover, we give some
examples to illustrate how to find the position vector from the intrinsic
equations of general helices.
