Consider the differential equation dy/dx= (y-1)/x. On the axes, sketch a slope field for the given differential equation at the nine points indicated.

Solution:

Lets first construct a table which contains the values of slope y’ = dydx = (y - 1)/x for 1 ≤ x ≤ 3, 0 ≤ y ≤ 2

For example when x = 1 and y = 0 then slope -1 which is the cell(1,1) of the table below. When x = 1 and y The cells contain the value of the slope for various values of x and y. The limits of x and y have already been given above.

These values of the slope are now plotted on an x-y plane which is called a slope field. Basically, slope fields are plotting small line segments of the slopes contained in the table above. The graph of the plot is given below:

Also, note that for y = 1 the slope of all the line segments is zero and that is why they are flat lines. The lowest level segments have negative slopes.

Consider the differential equation dy/dx= (y - 1)/x. On the axes, sketch a slope field for the given differential equation at the nine points indicated.

Summary:

The differential equation dy/dx= (y - 1)/x is plotted below on a graph which is basically called a slope field.