- #1

Saladsamurai

- 3,020

- 7

**Problem**

Instead of using arrows to represent vector functions, we sometimes use families of curves called

*field lines*. A curve y = y(x) is a field line of the vector function

**F**(x,y) if at each point (x

_{o}, y

_{o}) on the curve,

**F**(x

_{o}, y

_{o}) is tangent to the curve.(a) Show that the field lines y = y(x) of a vector function

**F**(x,y) =

**i**F

_{x}(x,y) +

**j**F

_{y}(x,y) are solutions of the differential equation

[tex]\frac{dy}{dx}=\frac{F_y(x,y)}{F_x(x,y)}[/tex]

--------------------------------------------------------------

(b) Determine the field lines of the function

**v**(x,y) =

**i**y +

**j**x

**Solution**

I know that the definition of

*field lines*is very similar, if not identical, to that of the curves in an integral field.

But I am really not sure, for part (a), how I am supposed to start. I am trying to show that y = y(x) is a solution to the diff eq, but I am only given the 'properties' of y(x). So I am a little confused as to how to start the math.

Any hints?

Casey