Since 2t = t + t, the following is a delay differential equation with variable delay -t, hence currently unsolvable by Mathematica.
In[44]:=
NDSolve[{2 y'[t] == x'[t], y[2 t] == 2 x[t], y[t /; t <= 0] == 0,
x[t /; t <= 0] == 0}, {y, x}, {t, 0, 4}]
During evaluation of In[44]:= NDSolve::cdelay: The method currently implemented for delay differential equations does not support delays that depend directly on the time variable or dependent variables.
There must be some way that Mathematica could be used to solve simple systems like this. I would really appreciate it if someone could help me out here.
Richard Jensen