I'm sorry for the delay, I was putting the pdf in English, if there is anything you don't understand you can ask.
Below is the resolution in ODE and the doubts about Laplace.
EDO is an abbreviation for ordinary differential equations.
I'll send what I've already done, by EDO. and then I will send as I tried to solve by Laplace and quote what I think is wrong.
The statement is: Find the currents of the circuit after the switch S is closed. I solved it by EDO (ordinary differential equations) and then I tried to solve it by Laplace and they gave different answers.