Question

How would i know the direction field of these DEs?
1. y' = 1
2. y' = t^2
3. y' = y
4. y' =t^2 +y^2
5. y' = y/t
6. y' = 1/t

Answer 1

Hmm, I don't really remember how to do direction fields.. maybe we can figure this out though..

Answer 2

So think about the first one a sec...
At every point, the derivative has a slope of 1.

If we were to integrate that function, we would get the family of functions y=t+c

Answer 3

When c=-1 we have a y-intercept of -1, so the line would look like this.

Answer 4

And the derivative at any point along that line (slope) would be 1, yes?