equation for stream's path
Hi, i'm new.
I have a question that gives me the equation of a hill:
I need to find an equation for the path of a stream that follows the path of steepest descent down the hill and passes through the point (1,1,5). I'm ok with the course material (i think, hehe) - that is, i realize that i'm working with gradients, partial derivatives, etc. If this was a "find the tangent plane or line" problem i'd be ok, but it seems to be a differential equation problem. In that case, i'm not sure how to make a differential equation out of it. It'd be great if someone could help.
P.S. We haven't learned integrals of any sort for multivariables yet...so path integrals are out (dunno if that helps).