I sit all day on a simple task and I still can't solve it. In the picture you can see the circuit it is about. I have to do the differential equation and solve it in a way that I can determine the voltage at the capacitor Uc(t). I have already solved RLC circuits, but I have problems with the parallel circuit between L2 and R3, which confuses me a lot. Can someone please help me? https://i.stack.imgur.com/TTxKu.jpg
This is my current approach: https://i.stack.imgur.com/zAiA1.jpg
My problem is that I can't just divide by L1 and L2. Using i_L2 = i - i_R3 doesn't give me a result either. So all my steps following the approach were/are unfortunately wrong.