When dealing with 2nd order ODE's with constant coefficients, you have this:
which you can get the characteristic equation like so:
Now, when dealing with Euler equations, you have this:
Here's where things get dicey.... When you have it in this nice form, you can get the characteristic equation like so:
However, if you have an Euler equation like this:
...now it's a lot nastier. How do you deal with Euler equations like this?
Can you just do a substitution like
...and revert it back at the end?