Can someone help me to solve this problem please. I can not solve it and i kinda figure it out how to solve..

 

Can someone help me to solve this problem please. I can not solve it and i kinda figure it out how to solve..

Well, if you kinda figure it out how to solve, then you need to kinda shows your work. We are not mind readers.

What if you didn't have to use Laplace Transforms? Could you solve it then? If so, what is the solution? That will give you something to check your Laplace-based solution against.

Can you simply the circuit any before you transform it?

What are the transforms for each element in the circuit -- including a capacitor with initial conditions?

 

Slightly better drawing...