I have the following circuit, and I need to graph V_out as function of V_in.
I have no information about the diodes and on V_2.
Can I assume that at t=0 diode 2 is open? if not where should I start?

 

V2 is probably your V_in. So, I think you want to graph V_out as a function of V_in.

Try different values of V_in and see how the circuit reacts.

What have you learned about diodes? Information about the particular diode may not be as important as the general model that can be used for simple calculations.

For more detailed information about the 1N4148 diode, you can find the datasheet online if you need it. It is a very common diode.

 

I have the following circuit, and I need to graph V_out as function of V_in.
I have no information about the diodes and on V_2.
Can I assume that at t=0 diode 2 is open? if not where should I start?

t=0 has nothing to do with it. There is no time involved in the problem at all.

You want to plot Vout as a function of Vin.

But you haven't defined what Vin is. My guess is that Vin = V2.

 

It if fairly easy to analyze. For simplicity, let's assume that those are ideal diodes - it just marginally simplifies the math.

1 v2 less than vbatt1. V2 and d1 can bebchopped off the circuit and you can calculate the current through the batt1, r2, d1, r1 and batt2, thus the output voltage.

2 when v2 is greater than vbatt1 but less than vbatt2, the voltage on where d1, d2 and batt1 meet is v2. Again, calculate the loop current.

3 when v2 is greater than vbatt2, d2 is reversely biased and output voltage is vbatt2.