Homework questions are definitely allowed on this site!! In fact, the major purpose of the site is to provide a place to discuss homework and other problems coming from class (like on review sheets) in detail. However, a good question will state the problem completely, using mathematical notation, and indicate any progress that the you've already made.
Example HW questions
Not so good
How do I do problem 5 on page 152?
A better question - we can improve the question by simply stating the problem.
Problem 5 on page 152 of our text asks us to solve the non-linear heat flow problem
$$
\begin{array}{cc}
(uu')' = 0 & 0 < x < \pi \\
u(0) = 0 & u'(\pi) = 1.
\end{array}
$$
I will admit that I am clueless on this problem - any suggestions?
Even better - Ideally we've made some progress on the problem, which we can state.
Problem 5 on page 152 of our text asks us to solve the non-linear heat flow problem
$$
\begin{array}{cc}
(uu')' = 0 & 0 < x < \pi \\
u(0) = 0 & u'(\pi) = 1.
\end{array}
$$
I see that I can integrate the differential equation $(uu')'=0$ to get
$$u\frac{du}{dx} = c,$$
where $c$ is a constant. This appears to be a separable ODE, but I'm having trouble remembering what to do with that. Any advice on how to proceed?
Other types of questions
Of course, other questions related to course material are welcome as well - but they must be directly related to our course and be specific, answerable questions. For example, problems out of the text but not directly assigned or from other source, but clearly related to our course, should be just fine. Open ended questions like "What's all this stuff good for, anyway?" are not a particularly good fit.
Questions about the operation of this site itself are also good; they should generally be tagged Meta.