Math: Calculus

Does anyone know how to do slope fields? I don't know how to do equations like dy/dx = 2y but I know how to do dy/dx = 2x. The "y"s confuse me. How do I do it? Thanks for any help!

To be honest, I'm confused about what's confusing you, so I don't know how much help I can be

Let's consider a set of 15 ordered pairs:
(0,2) (1,2) (2,2)
(0,1) (1,1) (2,1)
(0,0) (1,0) (2,0)
(0,-1) (1,-1) (2, -1)
(0,-2) (1,-2) (2,-2)

Given y'=slope=2y, we note the slope at these points:
4 4 4
2 2 2
0 0 0
-2 -2 -2
-4 -4 -4

(Poorly) graphically represented, with slopes (4,2,0,-2,-4) given (/,↗,-, ↘,\):

 2  / / /
 1  ↗ ↗ ↗
 0  - - -
-1  ↘ ↘ ↘
-2  \ \ \ 

    0 1 2

Over more points, we see trends comparable to the graphs of y=1*e^2x, y=0*e^2x, and y=-1*e^2x. In fact the general solution to y'=2y is y=C*e^2x.
Hope this helps...

Please restate; I don't understand what you're asking for either. What's this "slope field" you're asking about? If you give us an idea, maybe we can help. It sounds like Vectors or three variables in a derivative to form a plane instead of a line, or something, but yeah. Just give us more of an idea. Your topic isn't too well defined, so I'm not sure what to say...^_^'

Sorry...

Originally Posted by mmmmm_PIE

To be honest, I'm confused about what's confusing you, so I don't know how much help I can be

Let's consider a set of 15 ordered pairs:
(0,2) (1,2) (2,2)
(0,1) (1,1) (2,1)
(0,0) (1,0) (2,0)
(0,-1) (1,-1) (2, -1)
(0,-2) (1,-2) (2,-2)

Given y'=slope=2y, we note the slope at these points:
4 4 4
2 2 2
0 0 0
-2 -2 -2
-4 -4 -4

(Poorly) graphically represented, with slopes (4,2,0,-2,-4) given (/,↗,-, ↘,\):

 2  / / /
 1  ↗ ↗ ↗
 0  - - -
-1  ↘ ↘ ↘
-2  \ \ \ 

    0 1 2

Over more points, we see trends comparable to the graphs of y=1*e^2x, y=0*e^2x, and y=-1*e^2x. In fact the general solution to y'=2y is y=C*e^2x.
Hope this helps...

Yeah, that helped thanks!

No problem!

If you don't mind me asking, were you really asked to sketch a slope field for y'(x)=2x? Cause to me that not only seems like an enormous waste of time, but also a good way to have students mistakenly associate Differentials with traditional Integrals.

Originally Posted by mmmmm_PIE

No problem!

If you don't mind me asking, were you really asked to sketch a slope field for y'(x)=2x? Cause to me that not only seems like an enormous waste of time, but also a good way to have students mistakenly associate Differentials with traditional Integrals.

Yeah. We finished studying integrals and antiderivatives and now we're doing slope fields. I got a bad grade on my antiderivative test and I have to go to the teacher I guess for help since the rest of the year is antiderivatives, yikes! I'm glad I'm not the only one that's in my class, in the boat hehe.