We solve this 2 ways:

1. Setting up the equations and getting SNB to help solve them.

2. Directly using SNB to solve the 2 equations simultaneously.

Solution 1

We use the basic formula:

Considering the left-hand loop, the flow of current through the 8 Ω resistor is opposite for and . We regard as having positive direction:

Now, we consider the right-hand loop and regard the direction of as positive:

We now solve (1) and (2) simultaneously by substituting into (1) so that we get a DE in only:

Solving using SNB gives:

The graph of our solution is:

Now, from equation (2), we have:

This is of course the same graph, only of the amplitude:

Solution 2 - Using SNB directly

If we try to solve it using SNB as follows, it fails because it can only solve 2 differential equations simultaneously:

But if we differentiate the second line as follows (making it into a differential equation so we have 2 DEs in 2 unknowns), SNB will happily solve it using Compute → Solve ODE... → Exact:

Exact solution is:

Note the curious extra (small) constant terms and .