I've attached both a problem and its solution

I don't get from where did they deduce that ic(0+) = 37.4mA ?

 

It is the norton current, 30V/800R=37.5mA

 

I got how did they did the source transformation but why doesn't a part of the current go through the 800 ohm resistor

 

The initial voltage across the capacitor is 0 so that gives zero voltage across the Norton resistor as well, meaning all the current goes through the capacitor.

The current in the inductor is the integral of voltage across it so must still be 0 if no time has passed.

 

That makes sense thank you.

Btw both of you referred to the case as being the norton equivalent, is there any significance to that ? (Other than just a name)

 

I said Norton resistor because the actual circuit is a different configuration. In the original circuit the 800 ohm resistor of course takes all of the current.