Let y = f(x) be the solution to the differential equation dy/dx = y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given ∆x = 0.5

Answer 1

I already did this for you.
You know that the slope of the secant is m=∆y/∆x
So, ∆y = m*∆x
But for small ∆x, ∆y/∆x ≈ dy/dx.
So, ∆y ≈ y' * ∆x
That means f(5.5) = f(5) + y' * 0.5
f(6) = f(5.5) + y' * 0.5
You know y' = y-x, so now just plug in your numbers and iterate the two steps