I came up with two formulas and have no Idea whether their correct. 1. ∀x(S(x)∧¬C(x)) 2. ∀x∃y(S(x)∧C(y)→DoesNotLike(x,y))
And then I have one a bit more complicated, that I can think of multiple ways how to formalize but have no way of knowing if correctly: Every student attends a class taught by a teacher that they dont like.
P.s. this is not my homework, just preparation for an exam.
You need to specify carefully what you're taking the predicates $\ S\ $ and $\ C\ $ to mean.
Presumably, $\ S\left(x\right)\ $ means "$\ x\ $ is a student". I think your first formulation would then be synonymous with the sentence given in the title if $\ C\left(x\right)\ $ were taken to mean "$\ x\ $ likes all courses he or she has ever joined, or will ever join", and the conjunction were to be replaced with implication:$^{\mathbf \dagger}$ $$ \forall x\left(S\left(x\right)\rightarrow \neg C\left(x\right)\right) $$ However, I can't think of any interpretation of $\ C\left(y\right)\ $ that would make your second formulation similarly synonymous with that sentence.
It looks like $\ C\left(y\right)\ $ in the second formulation was intended to mean "$\ y\ $ is a course", but if that were so, there wouldn't appear to be anything in that formulation to specify that the course $\ y\ $ is one that student $\ x\ $ has joined or will join at some time. This could be partly rectified by making $\ C\ $ a two-place predicate for which $\ C\left(x,y\right)\ $ means "$\ y\ $ is a course which $\ x\ $ has joined or will join at some time", but even that's not enough to make the second formulation synonymous with the target sentence.
A second problem with the second formulation is the placement of the predicate $\ C\ $ before, rather than after, the implication.$^{\mathbf *}$ As written, the sentence $$ \forall x\exists y\left( S\left(x\right) \wedge C\left(x,y\right)\rightarrow\mbox{DoesNotLike}\left(x,y\right)\right) $$ merely says that for every student there is some course that the student wouldn't like if he or she were to join it. It does not assert that every student will, in fact, join such a course at some time. This can be rectified by placing the predicate $\ C\ $ after the $\mbox{implication:}^{\mathbf *}$ $$ \forall x\left( S\left(x\right) \rightarrow\exists y\left( C\left(x,y\right)\wedge\mbox{DoesNotLike}\left(x,y\right)\right)\right)\ \ . $$ As now formulated the predicate $\ C\ $ represents an existential statement which could be further spelt out by putting $\ C\left(x,y\right) = \exists t\,J\left(x,y,t\right)\ $, where $\ J\left(x,y,t\right)\ $ is taken to mean "$\ y\ $ is a course which $\ x\ $ joined, or will join, at time $\ t\ $. The last formulation above would then become: $$ \forall x \left( S\left(x\right) \rightarrow\exists y\exists t\left( J\left(x,y,t\right)\wedge\mbox{DoesNotLike}\left(x,y\right)\right)\right)\ \ . $$
* Edit: Thanks to Daniel Schepler, in his comment below, for pointing out an error in my original attempt to rectify this deficiency.
$\mathbf\dagger$ Further edit: I forgot that the first formulation suffered from the same problem as my first attempted rectification of the second.