Question

Sketch the direction field of the differential equation : dx/dt = 2t

Your assistance is appreciated.

Answer 1

I have a good idea, but I am not so sure how steep to make the slopes. Also is t on the x axis and x on the y axis?

Answer 2

x' is only proportional to t
when t=1/2, dx/dt=1 so that will be a line at a 45 degree angle with the x-axis
this thing should only get steeper as we move to the right along t...

Answer 3

okay

Answer 4

we can also see that at t=0, dx/dt=0 so that will be horizontal lines