I'm currently taking Physics II and I'm tasked to solve for the voltage $$U\_R(t)$$ in this circuit.

[![The RLC-Circuit](https://i.stack.imgur.com/PXu7h.png)](https://i.stack.imgur.com/PXu7h.png)

It's driven by a current source $$I(t) = I\_0\*e^{i\*\omega\*t}$$ and I can neglect the switch on process.
I'm currently at the point of having the differential equation to solve this problem but I'm not entirely sure on how to solve it yet. 

I wanted to ask if my thought process was correct so far and if I landed at the correct differential equation or am I on the completely wrong path?

[![enter image description here](https://i.stack.imgur.com/knA0Z.png)](https://i.stack.imgur.com/knA0Z.png)