We have just had an introduction to differential equations, and I need a little help as I left a bit confused and am still fumbling around with two problems:

Suppose and that

What does this say about k and C?

At this point, I thought that and that could be any value at all, but there are apparently two different answers and I am not sure if what I had mentioned before is even correct.

The other one that I am having troubles with is:

I found that the general solution was , but the problem asks for a second solution that might not be a general solution and which may have a different value of n than the one that was previously found. Could the answer be or is there an other answer that I am just not thinking of?

Thanks for the help everyone.