How important really is Differential Equations?

[blockRed]

Differential Equations isn't really used, but often the reason its valuable is that in a basic differential equations course, you will learn what a difference equation is. Difference equation is crucial to anyone doing finance, or empirical macroeconomics. They are used in Time Series Econometrics, which is the key tool for these subjects. If you don't have diff eq, I really wouldn't worry about it. I would however make sure I knew difference equations from Chiang, or Enders.

This is what I thought, but I was surprised to see how prominently it was mentioned on admissions websites.

It may be listed since most math major requirements have you take Diff Eq .

Could be (one reason) why it is mentioned as often as it is.

[Nichter]

"I don't think Diff Eq is hard"

You are mistaken. You definitely need very good knowledge of diff equations, calculus and linear algebra for PhD in Economics. I strongly recommend you look further into that. It is not simply solving ODEs (some ODEs can actually be quite tricky), there are several SDEs that come up especially in economics related to finance.

[OneArmedEcon]

For me, the main advantages of ODE were:
a) review and practice of integration methods (the details for which I had long since forgotten)
b) it makes Fourier transforms feel a little less intimidating if you are comfortable working with LaPlace transforms