Parametric Representation of Field Lines

[Icebreaker]

$$F(x,y,z)=(-\frac{y^2+2z^2}{x^2},\frac{2y}{x},\frac{4z}{x})$$

"Find parametric representations of the field lines."

How do I parametrize all possible field lines?

 

[HallsofIvy]

What field? I really wish people would give the entire exercise!

First of all, a "field" in the sense meant here is a physics concept, not a mathematics concept- you can have an electric field, a magnetic field, or a gravitational field! There is a mathematics "field" but it doesn't have lines!

Secondly, since you are posting this in Homework and Coursework forum, surely you know that you must show us what you have attempted on the problem yourself (which would help us figure out what in the world you are talking about!). IF I am interpreting this problem correctly, there are some very difficult parts to it. Getting started should be easy! What "field" do you have here and what are "field lines"?
You have given us a function of three

 

[Icebreaker]

Vector fields don't have lines? At least I think this is a vector field. This is an ad cal class and my assignment is as I typed it. I don't think it's asking for any sort of algebraic "fields" or "rings". But these days everything from every class is popping up in every other class, so I'll never know.

On what I've done: I can show that this field is conservative because it's the gradient of the function

$$\frac{y^2+2z^2}{x}$$

if that helps.