Thank you so much for that. It helped a lot to see that step worked out. Sorry for asking again, but could you possibly take a look at what I've done here and tell me where I'm going wrong? I'm sure it's something stupid.

I'm working on solving

Once again, the equation is hyperbolic so I found appopriate substitutions to be

and

So, taking the derivatives I find

Plugging these back into the pde, I end up with the equation (in canonical form),

I tried integrating with respect to eta to get

For some arbitrary B. However, I can't solve this ODE. I tried using an integrating factor, but that got messy quickly. I might have made an algebraic mistake in the reduction, but I've gotten the same canonical form twice.

If someone could take a look and show me where I went awry, I'd be most apprecitive.