So, I am trying to attempt part b of this problem using my answer from part a. I just want to confirm if I did part a correctly and how I can do part b?
2026-03-25 09:28:34.1774430914
How can I use Euler's Method in order to find the value of a constant k given the differential equation?
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hint
There are two possibilities :
with Euler after, $\; $ at $ x=0 $, the equation is $$f'(0)=\frac{f(1)-f(0)}{\Delta x}=2f(0)+1$$
thus $ k=-\frac 13.$
Euler before, $\; $ at $ x=1 $, gives
$$f'(1)=\frac{f(1)-f(0)}{\Delta x}=3+2f(1)+1$$ hence $ k=- 4$.