Question

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

dy/dx = y-x
This is just a linear DE, with solution
y = ce^x + x + 1

Using Euler's method,
f(x+h) = f(x) + f' * h
We need two steps to get from x=5 to x=6, so
f(5.5) = f(5) + (5-1)(0.5)
f(6) = f(5.5) + (f(5.5)-1.5)/0.5

Answer 2

oobleck that is wrong