Please see this article on how to use the results of DSolve and related function. Please see this article on this subject :
http://support.wolfram.com/kb/3825Your notebook uses NDSolve. Use DSolve instead for simple equations like this.
Clear["Global`*"]
Vs[t_] = 5 UnitStep[t];
R1 = R2 = R3 = 0.1; c = 1;
eqn1 = (Vs[t] - Vc1[t])/R1 == c*Vc1'[t];
eqn2 = (Vc1[t] - Vc2[t])/R2 == c*Vc2'[t];
eqn3 = (Vc2[t] - Vc3[t])/R3 == c*Vc3'[t];
sol1 = DSolve[{eqn1, Vc1[0] == 0}, Vc1[t], t]
Vc1[t_] = Vc1[t] /. First@sol1
sol2 = DSolve[{eqn2, Vc2[0] == 0}, Vc2[t], t]
