Okay, here is what it looks like:

The problem is stated as:

Set up a system of differential equations with initial conditions to describe the currents and in the electrical network. Assume is 100V, is 20 ohms, is 40 ohms, L_1 is 0.01 H and is 0.02 H. Currents are initially zero.

My work:

Kirchhoff's Law

After this, I can take it from there...but am I setting it up right? How do you set it up?