Thread: How do you get the characteristic equation of trickier Euler equations?

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?