@Rohit: I introduced
Join[Take[solv, 4], {1, 1, 1, 1}]
in a post far above to have easy acces to the "dashed lines" by then using (see p3 far above)
Join[{1,1,1,1},Take[solv, - 4]]
avoiding to have to change (which of course could be done as well)
PlotStyle -> Table[If[ i <= 4, {Red, Thickness[.01]}, {Blue, Thickness[.008], Dashed}], {i, 8}]]
and knowing that Log[1] == 0 will coincide with the x-axis and not disturb the plot.
Abyi wanted to have thick and dashed lines.
It seems that this is not necessary later on.
@Abiy : By the way, you said
I would like to plot V and VNI together as V+VNI
Look at your equations and initial values (with the input in the code above):
In[40]:= eee = Flatten[Table[eqn1g[i, j], {i, 2}, {j, 2}]];
Select[eee, MemberQ[#, VNI'[t]] &]
Select[eee, MemberQ[#, VNI[0]] &]
Out[41]= {
\!\(\*SuperscriptBox["VNI", "\[Prime]",
MultilineFunction->None]\)[t] == -6 VNI[t],
\!\(\*SuperscriptBox["VNI", "\[Prime]",
MultilineFunction->None]\)[t] == -6 VNI[t],
\!\(\*SuperscriptBox["VNI", "\[Prime]",
MultilineFunction->None]\)[t] == -6 VNI[t] + 0.116 x[t],
\!\(\*SuperscriptBox["VNI", "\[Prime]",
MultilineFunction->None]\)[t] == -6 VNI[t] + 1.45 x[t]}
Out[42]= {VNI[0] == 0, VNI[0] == 0, VNI[0] == 0, VNI[0] == 0}
The first two VNI can be integrated immediately giving
VNI[t_] := VNI[0] Exp[- 6 t]
and with
VNI[0] == 0
this is always zero (check it with the results of NDSolve).
A similar direct integration is possible for the last two V's