them meaning of Zero Input Response

the meaning of Zero Input/State Response question..

https://i48.tinypic.com/2j60m0.jpg

zir:
i cant understand how after turning to zero all the sources we get
this little circuit??

and we have to states
of what time we do this thing
?

zsr:
https://i49.tinypic.com/2l95r48.jpg

i know that i am supposed to do the homogeneos equation for this diff equation.

but i was told that ZSR is the state of the circuit in infinity
and we dont care about the initial condions.

then why we use the initial conditions if we dont care about them?

is the answer?

Vc=4 - 3e^(-t) for all the time

The answer is:

vc(t) = 1 + 3*exp(-t)

You should check your solution. The diff equation must use the initial conditions so it can be solved.