Question

How to draw direction field for the given differential equation? This behavior depends on the initial value of y at t=0 describe the dependency

Answer 1

y'=-2+t-y, I'm confused b/c theres a t in this equation

Answer 2

Ah, this is an inhomogeneous diffeq. The t-2 term is a "forcing function." Gimme a sec, I need to brush off the dust on this subject.

Answer 3

Alright don't think I have heard of the term forcing function

Answer 4

Are you still working on it?

Answer 5

Isn't the graph like y vs t maybe we pick what t is and the value of y to find y'?

Answer 6

Ok, sorry that took so long.

Don't worry about what I said about inhomogenous/forcing function stuff. It's not necessary for this problem.

Yeah, the easiest way is to just assume a value of t = 0, 1, 2, 3 ... etc. and plot multiple graphs.

It took me a while because I was attempting to solve for y(t), but that's more complicated than what the problem is asking for.

Answer 7

Okay thanks for your help and time!!! I probably will eventually have to learn forcing function lol

Answer 8

Oh, plot them all on the same graph, so the "dependency" is clear. You should see lines that get steeper in slope as time increases.

Answer 9

It's going to look something like this. All I did is evaluate y' at each point (y,t), and draw the slope. For example, at (y=1, t=1), y' = 2 - 1 -1 = 0, so I drew a flat line. Hope this helps.

Answer 10

Okay that makes a lot more sense thanks a lot for your help!! Really appreciate it

Answer 11

it's similar except you forgot the negative on 2 so it's just reflection of what you do on the y axis