Question

The general solution of the differential equation is given. Use a graphing utility to graph the particular solutions for the given values at C.
4xy'-x = 0
4y^2 - x^2 = C
C = 0, C = +/- 1, C = +/- 4

Answer 1

Are you being asked to draw a directional field for the given differential equation?

Answer 2

I guess so?
The general solution of the differential equation is given. Use a graphing utility to graph the particular solutions for the given values at C.
^^ That's the entire question.

Answer 3

You know you can draw this by hand also, though it's a bit tedious. The solution to differential equation isn't too complex.
But if you're being asked to use a program, I suggest using Mathematica or MatLab. I can probably guide you better if you have MatLab, but not 100% sure on mathematica since they changed the software and it's commands.

Answer 4

i have a graphing calculator...?

Answer 5

but then what's the differential equation used for..?

Answer 6

Lol. I don't know how to use graphing calculator. I've honestly never used one in a math class. But I can help you draw it by hand.

Answer 7

The directional field basically tells you the solution to your differential equation without solving it. I think they are basicallly asking you to show that it's the correct solution without actually solving the differential equation because that's what directional field (also known as vector field) really is.

Answer 8

so basically just graph the 4y^2 - x^2 = C using the given C's and that's it?!?!

Answer 9

Well, I think you know what the graph of 4y^2-x^2 is, right? I believe it's a circle.
So you draw lines around a plane: