An example...
	y ' = y - x,    y(0) = 2 (this is the example we graphed before). We'll use  Dx = 0.1  The choice of  Dx is usually dictated by the problem or the situation.  The smaller  Dx is the more accurate the approximated solution will be, but of course you need to do more work to cover an interval of a given length. For the first step, we can use that x=0 and y=2, therefore  y ' = 2.  Euler's method then tells us that:             y(x + Dx) = y(x) + f(x,y) Dx                                   y(0.1)    =  1    + (2 - 0) 0.1  = 1.2