The main thing you need to know about "Euler-type" equations is that there is a "one-to-one" correspondence between them and equations with constant coefficients.

Just as you can "look for" solutions to equations with constant coefficients using (even though solutions may not be exponential), so you can "look for" solutions to "Euler-type" equations using .

That's because the change of variable x= ln(t) will change an "Euler-type" equation in variable t to an equation with constant coefficients in variable t.

For example, is an "Euler-type" equation in variable t. If we let x= ln(t), then .

Further .

So .