Please no b.s. answers like giving a wiki page.... for euler\'s method...for dy/

Question

Please no b.s. answers like giving a wiki page.... for euler's method...for dy/dx=f(x,y) and y(x0)=y0, we start at x0,y0 and take the slope f(x0,y0) to use to approximate the next point y(x1)...but we supposedly end the first line at x1,y1...my question is ...if we end the line at x1,y1 then f(x1,y1) must equal f(x0,y0) which doesn't make sense given the circumstances....but if we start a new line at x1,y1 then it still doesn't make sense because the equation y1=y0 + hf(x0,y0) would imply that the difference between y1 and y0 is just h* the slope at x0,y0 which can't be the case if at x1,y1 there is a different slope im basically asking for the polygonal broken line method of approximating the solution...is the next point the end of the first line or the start of the new line...it cannot be both

Explanation / Answer

we consider two points which are so close such that the differnce between them is small . this method is more efficient when the interval ---> 0 , when interval is high it is inefficient in euler's method we do the same , we consider a ponit and to find out other point we add slope at first point x distance between two points to first point plaese rate me

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