Non-ideal transformer transient state

So, I've encountered a problem that doesn't look that hard, but I simply can't solve it. I have a simple non-ideal transformer circuit and I want to compute V_0. What I was able to find so far are the equations for each loop.

For t >= 0:

Loop 1:

i_1 + 2*(i_1)' + (i_2)' = 6

Loop 2:

3*(i_2)' + 2*i_2 + (i_1)' = 0

• Can you be very formulaically (or numerically) clear about what the voltage source actually is? Dec 12 '21 at 15:36
• u(t) is a unit step function, which for t<0 it is 0 and for t>=0 its value is 1. So the voltage source is a step function which for t>=0, its value is 6V DC Dec 12 '21 at 15:38
• Is it this: t>=0 its value is 1 or is it this: t>=0, its value is 6V DC Dec 12 '21 at 15:47
• t>=0, its value is 6V DC Dec 12 '21 at 15:49

Here's a hint on how to find $$\I_1\$$
Does that help you get started? $$\I_2\$$ will be the current flowing through the 1.3333 Ω resistor, divided by the inverse of the turns ratio (1.5).