zir zsr question

when do we use ZSR ZIR

i saw how we solve a first order diff equation
mathematickly
by particular solutions and homogeneous
and suming them


and they didnt use ZIR ZSR at all

why?

when do we use ZIR ZSR?

Well, maybe you don't notice that, but when you solve the differential equation, you are using the initial conditions to reach a final state, so ZIR and ZSR are used there.