First of all, there is NO given time-dependent information. Why do you want I(D) for t<0 and t>0? I assume you want the I(D) for the
diode's working point.
It would be better understood if we plug in some values. Here we go:
Given:
[tex]R_{1}=R_{2}=R_{3}=100\Omega[/tex]
[tex]I_{0}=24\ mA[/tex]
By considering the open (oc) and short circuits (sc), you will obtain two values where:
[tex]I_{oc}=0[/tex] as [tex]V_{oc}=V_{Th}=1.2\ V[/tex]
[tex]I_{sc}=\frac{V_{Th}}{R_{Th}}=8.0\ mA[/tex]
Here is the I-V source characteristic, the red line:
Now, if the characteristic of the diode is given by
Then plotting the characteristic on the same graph gives the green line:
A. Graphically
So you know that the intersection is the working point for the diode and there you can write down the value of [tex]V_{D}=0.9\ V[/tex] and [tex]I_{D}=2.0\ mA[/tex].
B. Numerically
Find the equation of the I-V source characteristic using the famous [tex]Y=mX+C[/tex] where you will expect C = 0.008 A and and negative slope m. Then, solving the simultaneous equations proves the values obtained in A. That's simple.