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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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?

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1 Answer

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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$.

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