Solving Old Midterm Problem: Voltage Across 9kΩ Resistor

[gfd43tg]

I am working on the second problem of an old midterm, and I cannot figure out how they got that answer for the voltage across that 9kΩ resistor. I said the current going through the resistor is the same as that going through the inductor, so I figured I would find the current as a function of time, then just multiply by the resistor value.

I posted the solution as well

 

[donpacino]

When you present a symbolic expression as an answer, you have to be sure that all symbols are defined. Also you want each symbol to be a non changing value. IL is a dynamic value. While your answer of Vo=IL*R3 is correct. it not the simplest. Find IL as a function of the input current, L, R1, R2, and R3

 

[NascentOxygen]

When t=0 the exp(-t/T) term equals 1.

So the expression you have for i becomes i(0) = i_∞ + ( i_∞ - i₀ )

This does not look right. You have a sign wrong, or something.