What diffy Q solving methods are most important?

[TomServo]

I'm trying to get a feel for what's important and what's not so important. For example is memorizing the Frobenius method important or is it something you don't use much? I'm asking from the perspective of a grad student.

 

[Mmm_Pasta]

Normally one would look up the general solution to some differential equation and then apply any initial conditions or boundary values. What you should focus is knowing what a differential equation is, how to set up a problem that will produce such equation (like what you do in mechanics), etc. You may need more or less depending what you personal interests and goals are. I wouldn't bother memorizing any particular method as you'll just forget it. Although, it would be helpful to be able to recognize that a differential equation has already been solved before that way you can look up the solution.