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

Answer 1

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:
https://tutor.hix.ai

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:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Charles Anctil

To draw the slope field of the differential equation ( y' = y - x ), you need to evaluate the expression ( y - x ) for various values of x and y. Then, at each point (x, y), you draw a short line segment with slope equal to the value of ( y - x ) at that point. Repeat this process for different values of x and y to sketch the slope field.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.