This fall I might be able to take both courses. According to our school's sample curriculum, both courses are taken simultaneously in upper sophomore year (spring). Of course it is upon the decision of the students.

My questions are: how hard are both courses? Should I take both? Between the two, which one looks more like a prerequisite (preparation) for the other?

If I were to give an opinion on which one were more "fundamental", then I'd say the linear algebra one. And that would certainly be the more useful subject to know (depending of course on what you intend to go on and do).

Methods of solving differential equations tend to be just that: a list of different methods which work in different cases. Although being able to solve differential equations is essential for a physicist, engineer etc, it won't help in any area other than differential equations. Linear algebra, on the other hand, is used all over the place.

What applications are you interested in? Some fields use linear algebra heavily (computer vision) and some field use differential equations heavily (control theory).

I am still not sure yet. But I believe as a computer engineering major (and also intended doing physics as well) I'd like to work in fields like electronic devices, such as microprocessor.

I guess I should say physics in general, but for career-wise, solid states, quantum physics.

"What applications are you interested in?"
I am interested in Linear algebra and defferential Equations although it is not really useable in any other fields of works. . .

What??? Both Linear Algebra and Differential Equations are used extensively in Physics, Chemistry, Biology, ... any science, as well as Economics and Business Administration!