How do you draw the slope field of the differential equation #y'=y-x# ?

1 Answer
Jan 21, 2015

You have to substitute values of #x# and #y# into your differential equation. The result will be the value of #y'# which represents the slope in that point of your function (solution of your differntial equation).
To draw these slope field may be a little bit challenging but you can use softwares that can help you to do that, such as the one from:

In your case you may use pencil and paper and draw at each point a little line with inclination representing the value calculated at that point.
Have a look at the drawing obtained from the above website using your equation:
enter image source here
Consider, for example, the coordinates:
#x=2# and #y=2#
You get #y'=y-x=2-2=0#
This means #slope=0# and you'll draw a vertical line (red circle in the next picture):
enter image source here

By hand you can draw less lines and speed up a little bit the process but I would suggest you to use the help of a software anyway.