My teacher did about lpf and he show us that that formula

from this circuit

my question is why is y(t)/R?
Thank you!!

 

Why not?
Can you say what is it that you do not understand?

 

My teacher did about lpf and he show us that that formula
View attachment 202092
from this circuit
View attachment 202093
my question is why is y(t)/R?
Thank you!!

Given (A+B)/C, do you not understand that this is equal to (A/C) + (B/C)?

 

My teacher did about lpf and he show us that that formula
View attachment 202092
from this circuit
View attachment 202093
my question is why is y(t)/R?
Thank you!!

Here is a hint:
Note that the capacitor and resistor are in series, and elements in series have the SAME current though both of them. Now consider the current through the cap vs the current through the resistor. You probably understand what the current through the cap is, but how do you calculate the current through the resistor.
That will give you your answer.

 

Why not?
Can you say what is it that you do not understand?

In his presentation, he is telling us that he is using Kirchhoff's law of current
I get that the input current(x(t)/R) in the junction A is that same as the output(C*y'(t)+y(t)/R) but the y(t)/R how does it get it?

 

No, no.
There is no output current.

Input current is the current through R which is
( x(t) - y(t) ) / R